使用并行分散隐式微分的快速电网排放敏感性计算
Fast Grid Emissions Sensitivities using Parallel Decentralized Implicit Differentiation
AI总结：
针对电网排放敏感性计算，提出并行分散隐式微分方法，避免显式雅可比矩阵，在500节点系统上实现超10倍加速。
摘要：
边际排放率——碳排放对电力需求的敏感性——对于评估减排措施的影响至关重要。与节点边际电价类似，节点边际排放率（LMEs）可能在地理上存在差异，即使是在邻近位置之间，并且可能由于储能和爬坡约束等原因而在不同时间段之间耦合。这种时间耦合使得在具有高储能和可再生能源渗透率的大型电力网络中计算LMEs在计算上代价高昂。最近的研究表明，分散算法可以通过在微分过程中解耦时间步长来缓解这一问题。不幸的是，我们证明这些潜在的速度提升被电力系统问题中固有的稀疏结构所抵消。我们通过引入一种并行的、反向模式的分散微分方案来解决这些限制，该方案从不显式实例化解映射的雅可比矩阵。我们在理论上和经验上都表明，在计算电网排放敏感性时，并行化对于实现非平凡的速度提升是必要的。在500节点系统上的数值结果表明，我们的方法相比集中式和串行分散方法可以实现超过10倍的速度提升。
英文摘要：
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.
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