Differentiable Electricity-Market Clearing for Gradient-Based Planning

Abstract

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.