在供热需求预测不确定性下的分布鲁棒调度
Distributionally Robust Scheduling of Electrified Heating Under Heat Demand Forecast Uncertainty
AI总结：
本文提出了一种分布鲁棒机会约束优化框架，用于在供热需求预测不确定性下的电锅炉日提前调度，通过校准模糊集和建模实时反弹成本，有效降低运营成本和需求违规风险。
摘要：
具有热存储的电加热系统，如电锅炉和热泵，代表了需求侧灵活性的主要来源。在当前的电力市场设计下，运营此类资产的平衡责任方（BRP）被要求提交具有约束力的日提前电力消费计划，并且他们通常基于热需求和电力价格的预测来执行。常见的调度方法隐含假设预测不确定性可以很好地用历史预测误差来表征。然而实际上，不确定性累积效应会在承诺计划无法执行时造成显著的不平衡价格风险。为此，我们提出了一种分布鲁棒机会约束优化框架，用于多兆瓦电锅炉的日提前调度，仅使用有限的残余预测样本。我们推导了问题的一个可处理的凸改写形式，并通过一个先验可调的风险参数直接从历史预测误差数据校准模糊集。数值结果表明，强制对热需求平衡约束施加性能保证，将需求违规减少40%，相比基于确定性预测的调度器，以及相对于具有固定误差分布的名义机会约束模型，最高可减少10%。进一步，我们表明，将需求违规的实时反弹成本作为第二阶段项进行建模，可以将整体日运营成本降低高达34%，通过对高度波动的日提前电力价格进行对冲。
英文摘要：
Electrified heating systems with thermal storage, such as electric boilers and heat pumps, represent a major source of demand-side flexibility. Under current electricity market designs, balance responsible parties (BRPs) operating such assets are required to submit binding day-ahead electricity consumption schedules, and they typically do it based on forecasts of heat demand and electricity prices. Common scheduling approaches implicitly assume that forecast uncertainty can be well characterized using historical forecast errors. In practice, however, the cumulative effect of uncertainty creates significant exposure to imbalance-price risk when the committed schedule cannot be followed. To address this, we propose a distributionally robust chance-constrained optimization framework for the day-ahead scheduling of a multi-MW electric boiler using only limited residual forecast samples. We derive a tractable convex reformulation of the problem and calibrate the ambiguity set directly from historical forecast-error data through an a priori tunable risk parameter. Numerical results show that enforcing performance guarantees on the heat-demand balance constraint reduces demand violations by 40% compared to a deterministic forecast-based scheduler and up to 10% relative to a nominal chance-constrained model with a fixed error distribution. Further, we show that modeling the real-time rebound cost of demand violations as a second-stage term can reduce the overall daily operating cost by up to 34% by hedging against highly volatile day-ahead electricity prices.
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