让电力市场出清可微，用梯度优化数据中心选址与负荷分配。
Differentiable Electricity-Market Clearing for Gradient-Based Planning
- 将市场出清建模为可微层，实现规划参数的梯度反传。
- 在36种工况下优化50MW负荷分配，最优解误差仅2.3%~8.5%。
- 适合需考虑电价动态的大型设施规划者使用。
大型数据中心的规划难题在于其规模会改变自身支付的电价，而电价由市场出清决定——这是一个随运行状态重新求解的约束优化问题。传统模拟只能评估方案性能，无法指导优化。本文将市场出清作为可微优化层：前向传播求解市场，反向传播通过已清电价将规划代价回传至设计方案。经有限差分验证后，应用于在两个合成网络中将50 MW负荷分配至六个候选母线，在固定每站点成本、覆盖36种运行状态的场景下进行优化。相比穷举所有站点组合，梯度优化几乎精确恢复连续分配，最差目标差距为最优与最差单站点成本差的2.3%和8.5%。其唯一系统性偏差具启发性：在站点应关闭的成本附近，离散站点数量的平滑松弛导致站点缩小而非关闭，使离散切换延迟。该方法使考虑市场的规划变为可梯度搜索的问题。
原文摘要 · Abstract (English)
Planning a large data center is difficult because a facility big enough to matter changes the electricity prices it will pay. Those prices are set by market clearing, a constrained optimization problem solved anew in every operating condition. However, simulating the market tells a planner how a candidate plan performs but not how to improve it. Here we treat market clearing as a differentiable optimization layer: each forward pass solves the market, and reverse-mode automatic differentiation propagates the planning cost back through the cleared prices to the plan. After validating these gradients against finite differences, we apply them to a concrete problem: allocating 50 MW of data-center load across six candidate buses in two synthetic networks, under a fixed cost per active site, evaluated over 36 operating states. Judged against exhaustive enumeration of all site combinations, gradient optimization recovers the continuous allocations almost exactly, with worst-case objective gaps of 2.3\% and 8.5\% of the cost difference between the best and worst single site. Its one systematic error is instructive: near the costs at which a site should close, the smooth relaxation of the discrete site count shrinks the site rather than closing it, so discrete transitions arrive late. Differentiable market clearing thus turns market-aware planning into a problem gradients can search.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。