复频率表示下电力系统同步恢复的性能极限与权衡

中文摘要 AI 辅助

电力系统同步研究主要关注同步能否实现，而一个补充问题是扰动后同步恢复的质量如何塑造。在逆变器主导的系统中，这种恢复涉及耦合的相角和电压幅值动态，而复频率为此提供了统一的表示。本文在该表示下建立了同步恢复的守恒定律。对于给定系统及其初始状态，所提出的恢复残差的对数积分由初始收缩率和右半平面（RHP）零点-极点结构固定。因此，除非这些项设定的预算发生变化，否则同步恢复性能无法在频率和变量上均匀改善；保持这些项的控制器调谐只能将残差响应在频率间重新分配。该守恒定律适用于满足温和解析条件的线性和非线性恢复响应。它进一步导出了有限频率峰值-带宽极限以及复频率平方恢复的时间域积分下界。系统级扩展将经典的Bode型灵敏度守恒作为LTI特例恢复。在异构IEEE 39节点系统上的研究验证了该理论。

英文摘要

Power-system synchronization studies mainly ask whether synchronization can be achieved, whereas a complementary question is how well post-disturbance synchronization recovery can be shaped. In inverter-dominated systems, this recovery involves coupled phase-angle and voltage-magnitude dynamics, for which complex frequency provides a unified representation. This paper establishes a conservation law for synchronization recovery in this representation. For a given system and its initial state, the logarithmic integral of the proposed recovery residual is fixed by the initial contraction rate and the right-half-plane (RHP) zero--pole structure. Hence, synchronization recovery performance cannot be improved uniformly over frequencies and variables unless the budget set by these terms changes; controller tuning that preserves them can only redistribute the residual response across frequencies. The conservation law applies to both linear and nonlinear recovery responses satisfying the mild analyticity conditions. It further yields finite-frequency peak--bandwidth limits and a lower bound on the time-domain integral of squared complex frequency recovery. A system-level extension recovers classical Bode-type sensitivity conservation as an LTI special case. Studies on a heterogeneous IEEE 39-bus system verify the theory.

发表机构

• Tsinghua University（清华大学）

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