周期负荷激励下的负荷能力极限
Loadability Limits Under Periodic Load Forcing
AI总结：
该研究针对周期变化的负荷，将静态负荷能力极限扩展到受迫周期轨道，发现其极限随激励频率变化，在四节点系统中静态裕度大幅缩小，不稳定性机制改变，静态分析无法捕捉这些效应。
AI中文摘要：
静态负荷能力极限被定义为平衡方程失去解时的需求值，是大型新负荷互联筛选的标准依据。本文表明，当部分需求随周期变化（如数据中心负荷）时，稳态为受迫周期轨道，其负荷能力极限与静态极限不同。经典优化论证从平衡态直接扩展到周期映射的不动点。在极限处，单值矩阵的弗洛凯乘子取+1，因此一般不稳定性是轨道的周期折叠，而非平衡态的鞍结。该极限因此是激励频率的函数，静态计算无法捕捉。此外，当网络雅可比矩阵沿周期变为奇异时，奇异诱导的不稳定性被扩展到轨道。在四节点测试系统中，静态裕度为2.5 p.u.，在摇摆频率附近缩小至0.53 p.u.，不稳定性机制从电压崩溃切换为功角折叠，冷启动在轨道仍存在的幅值下失败，静态分析无法再现这些效应。
英文摘要：
The static loadability limit, defined as the demand at which the equilibrium equations lose their solution, is the standard basis for interconnection screening of large new loads. This letter shows that when part of the demand varies periodically, as for data-center loads, the steady state is a forced periodic orbit whose loadability limit differs from the static one. The classical optimization argument is extended directly from equilibria to fixed points of the period map. At the limit, the monodromy matrix acquires a Floquet multiplier at +1, so the generic instability is a cyclic fold of the orbit rather than a saddle-node of equilibria. The limit is therefore a function of the forcing frequency, which no static computation can capture. Additionally, with the network Jacobian turning singular along the cycle, singularity-induced instability is extended to orbits. On a four-bus test system, a static margin of 2.5 p.u. shrinks to 0.53 p.u. near the swing frequency, the instability mechanism switches from voltage collapse to a rotor-angle fold, and cold starts fail at amplitudes where the orbit still exists. A static analysis reproduces none of these effects.
