无需梯度更新,用统计方法快速适配电力潮流模型应对线路故障。
Gradient-Free Topology Adaptation for Power Flow Surrogates via In-Context Whitening

- 基于基础拓扑的前两阶统计量进行输出空间白化,实现梯度自由适配。
- 在多个系统上误差降低6至28倍,最坏节点功率失衡减少30倍。
- 适合电力系统实时仿真,部署快且可并行于普通CPU上运行。
用于交流潮流(ACPF)问题的机器学习代理模型虽能摊销固定网络重复求解的成本,但当线路故障导致拓扑变化时,精度下降一到两个数量级,这是由操作者偏移引起的。输入输出映射因导纳矩阵改变而变化,相同输入产生不同输出分布。现有方法依赖目标拓扑数据和每拓扑的梯度步长进行修正。本文提出无梯度统计修正方法——上下文白化(ICW),将ACPF代理模型在基线拓扑的前两阶矩白化后的输出空间中训练,并通过新拓扑上少量几百次求解结果重新估计白化参数,从而实现无梯度、无权重、架构无关的适配。我们证明,在仿射白化器中唯一保持物理输出向量坐标语义不变的是ZCA白化,因此在高效可逆修正中,仅需两阶矩即可。在IEEE 30、118和300节点系统下,面对N-1与N-2故障,ICW相比冻结代理模型整体误差降低6~28倍(单量纲最高达54倍),最坏节点功率平衡偏差减少高达30倍,且在三种骨干网络上均表现一致。部署规模下,其精度媲美甚至超过基于梯度的适配,同时速度提升21~34倍,计算成本可并行于通用CPU核心,无需每个故障场景配备一台GPU。
原文摘要 · Abstract (English)
Machine-learned surrogates for the AC power flow (ACPF) problem amortize the cost of repeated solves on a fixed network, but lose one to two orders of magnitude of accuracy when a line outage changes the topology. This degradation is an operator shift. The altered admittance matrix changes the input-to-output map, so identical inputs yield a different output distribution. Existing methods correct this with target-topology data and per-topology gradient steps. We ask whether the correction can instead be made statistical and gradient-free. We propose In-Context Whitening (ICW), which trains an ACPF surrogate in an output space whitened by the base topology's first two moments, and adapts it to an unseen N-1 or N-2 topology by re-estimating that whitening from a few hundred solved cases on the new topology. This adaptation is gradient-free, weight-free, and architecture-agnostic. We prove that among affine whiteners the unique choice that preserves the coordinate-wise semantics of the physical output vector is ZCA whitening, so within efficient invertible corrections, two moments are sufficient. Across the IEEE 30-, 118-, and 300-bus systems under N-1 and N-2 contingencies, ICW reduces overall error by 6$\times$ to 28$\times$ over frozen surrogates (up to 54$\times$ per-quantity under N-2) and cuts worst-bus power-balance mismatch by up to 30$\times$, with consistent gains across three backbones. At deployment scale it matches or beats gradient-based adaptation in accuracy while adapting 21$\times$ to 34$\times$ faster, with a cost that parallelizes on commodity CPU cores rather than requiring one GPU per contingency.
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