用于基于梯度规划的可微分电力市场出清

中文摘要 AI 辅助

规划大型数据中心颇具难度，因为规模足以产生显著影响的设施会改变其需支付的电价，而这些电价由市场出清（一种在每种运行工况下重新求解的约束优化问题）设定。然而，模拟市场只能告知规划者候选方案的表现，却无法指导其改进。本文将市场出清视为一个可微分优化层：前向传播求解市场，反向模式自动微分将规划成本通过出清价格反向传播至规划方案。在通过有限差分验证这些梯度后，我们将其应用于具体问题：在两个合成网络中，将50兆瓦（MW）的数据中心负载分配至6个候选母线，在固定活跃站点成本下，对36种运行状态进行评估。与所有站点组合的穷举搜索相比，梯度优化几乎能精确恢复连续分配，最坏情况下的目标差距为最佳与最差单站点成本差值的2.3%和8.5%。其唯一系统性误差具有启发意义：在站点应关闭的成本附近，离散站点数量的平滑松弛会缩小站点规模而非关闭它，因此离散转换出现较晚。由此，可微分市场出清将感知市场的规划转化为可通过梯度搜索求解的问题。

英文摘要

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.

发表机构

• Macrocosm Inc.（宏宇宙公司）
• Institute for New Economic Thinking, University of Oxford（牛津大学新经济思维研究所）

机构由 AI 辅助整理，请以论文原文为准。

补充信息

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9 pages, 4 figures