标题： 电力需求不确定下的鲁棒连续时间发电调度：仿射决策规则方法 显示英文标题

标题： Robust Continuous-Time Generation Scheduling under Power Demand Uncertainty: An Affine Decision Rule Approach

摘要： 大多数针对需求不确定性的电力系统发电调度模型依赖于基于能量的有限时间段公式化方法，这种方法可能无法确保电力供应与需求在时间上连续平衡。 为了解决这个问题，我们提出了一种在连续时间框架下的鲁棒发电调度模型，采用决策规则方法。 首先，对于一组给定的需求轨迹，我们制定一个通用的鲁棒发电调度问题，以确定将这些需求轨迹和时间点映射到发电机功率输出的决策规则。 随后，通过精心设计一类当前需求下仿射的决策规则，其中系数随时间不变且常数项为时间的分段连续仿射函数，我们推导出该问题的一个替代模型作为我们的模型。 因此，我们的模型可以重新表述为一个有限维线性规划问题，用于确定每个断点处系数和常数项函数值，可通过割平面法求解。 与大多数现有使用伯恩斯坦多项式的连续时间模型不同，我们的模型是非前瞻性的，使其更具实用性。 我们还提供了说明性的数值示例。 显示英文摘要

摘要： Most existing generation scheduling models for power systems under demand uncertainty rely on energy-based formulations with a finite number of time periods, which may fail to ensure that power supply and demand are balanced continuously over time. To address this issue, we propose a robust generation scheduling model in a continuous-time framework, employing a decision rule approach. First, for a given set of demand trajectories, we formulate a general robust generation scheduling problem to determine a decision rule that maps these demand trajectories and time points to the power outputs of generators. Subsequently, we derive a surrogate of it as our model by carefully designing a class of decision rules that are affine in the current demand, with coefficients invariant over time and constant terms that are continuous piecewise affine functions of time. As a result, our model can be recast as a finite-dimensional linear program to determine the coefficients and the function values of the constant terms at each breakpoint, solvable via the cutting-plane method. Our model is non-anticipative unlike most existing continuous-time models, which use Bernstein polynomials, making it more practical. We also provide illustrative numerical examples.