Fast Grid Emissions Sensitivities using Parallel Decentralized Implicit Differentiation

TL;DR

This paper introduces a parallel decentralized implicit differentiation method to efficiently compute locational marginal emissions rates in large, complex power systems, significantly reducing computation time.

Contribution

The paper presents a novel parallel, reverse-mode decentralized differentiation scheme that avoids explicit Jacobian computation, enabling faster sensitivity analysis in large-scale power networks.

Findings

Achieves over 10x speedup on a 500-node system.

Parallelization is essential for meaningful speedups.

Addresses limitations of previous decentralized algorithms.

Abstract

Marginal emissions rates -- the sensitivity of carbon emissions to electricity demand -- are important for evaluating the impact of emissions mitigation measures. Like locational marginal prices, locational marginal emissions rates (LMEs) can vary geographically, even between nearby locations, and may be coupled across time periods because of, for example, storage and ramping constraints. This temporal coupling makes computing LMEs computationally expensive for large electricity networks with high storage and renewable penetrations. Recent work demonstrates that decentralized algorithms can mitigate this problem by decoupling timesteps during differentiation. Unfortunately, we show these potential speedups are negated by the sparse structure inherent in power systems problems. We address these limitations by introducing a parallel, reverse-mode decentralized differentiation scheme that never explicitly instantiates the solution map Jacobian. We show both theoretically and empirically that parallelization is necessary to achieve non-trivial speedups when computing grid emissions sensitivities. Numerical results on a 500 node system indicate that our method can achieve greater than 10x speedups over centralized and serial decentralized approaches.