标题： 在机组组合问题中实现通用阶次频率动态响应模型和频率偏移持续时间准则 显示英文标题

标题： Implementing General-Order Frequency Dynamic Response Model and Frequency Excursion Duration Criterion in Unit Commitment Problem

摘要： 本文介绍了一种新颖的方法，通过通用阶微分方程模型将频率动态纳入单位组合（UC）问题中，并使用伯恩斯坦多项式逼近进行求解。 传统的频率约束UC（FCUC）模型通常依赖于简化的第一阶假设或标量频率指标，如频率最低点，以间接实现动态行为。 相比之下，我们的公式明确使用二阶动态对时域频率响应进行建模，从而能够更准确和灵活地表示发电机行为。 所得的微分方程通过伯恩斯坦多项式以高保真度进行逼近，导致一个混合整数线性规划（MILP）公式，该公式对于小规模电力系统仍具有计算可行性。 此外，我们引入了一个新的约束条件，基于低于临界阈值的频率偏差持续时间，这是由继电器操作和设备保护等实际问题所驱动的。 采用一种数据驱动的方法，将该阈值下的面积（即伯恩斯坦逼近的积分）与频率偏差的持续时间相关联。 所提出的框架使用西班牙一个孤岛系统的实际数据进行了验证，结果表明在运营成本适度增加的情况下，频率安全性得到了增强。 这些结果表明，该方法在低惯性、小规模电力系统中具有很强的应用潜力。 显示英文摘要

摘要： This paper introduces a novel approach for incorporating frequency dynamics into the unit commitment (UC) problem through a general-order differential equation model, solved using Bernstein polynomial approximation. Traditional frequency-constrained UC (FCUC) models typically rely on simplified first-order assumptions or scalar frequency metrics, such as frequency nadir, to indirectly enforce dynamic behavior. In contrast, our formulation explicitly models time-domain frequency response using second-order dynamics, enabling a more accurate and flexible representation of generator behavior. The resulting differential equations are approximated with high fidelity using Bernstein polynomials, leading to a mixed-integer linear programming (MILP) formulation that remains computationally tractable for small-scale power systems. Additionally, we introduce a new constraint based on the duration of frequency excursions below a critical threshold, motivated by practical concerns such as relay operation and equipment protection. A data-driven method is employed to relate the area under this threshold-computed as the integral of the Bernstein approximation-to the duration of frequency deviation. The proposed framework is validated using real-world data from an island system in Spain, demonstrating enhanced frequency security with a moderate increase in operational cost. These results suggest the method's strong potential for application in low-inertia, small-scale power systems.