电力系统的广义H矩阵稳定性
Generalized H matrix stability for power systems
AI总结：
本文针对电力系统小信号稳定性，提出了适用于任意负荷位置的广义H矩阵稳定性判据，通过2869母线系统案例验证，其稳定性评估准确且计算速度较雅可比方法提升340倍，优于NRPS模型。
摘要：
本文研究了带有任意负荷的电力系统模型的小信号稳定性，重点关注无损网络中局部恒定功率负荷的情况。所提分析的核心要素是矩阵H，它表示发电机功率相对于其相对角度的偏导数。若负荷消耗局部恒定功率，则任意平衡点的局部稳定性由H的性质决定：具体而言，当H为正定矩阵时，平衡点渐近稳定；当H满秩且非正定时，平衡点不稳定。本文还建立了H的特征值与系统雅可比矩阵之间的若干定量关系。主要贡献在于允许负荷任意分布在输电网络中，从而推广了现有的H矩阵稳定性判据，该判据仅在负荷与发电机位于同一母线时有效。通过涉及多达2869个母线的系统案例研究，证明了所提判据的优势：它能保持准确的稳定性评估，而NRPS模型等替代方法被发现过于保守；此外，与基于雅可比矩阵的方法相比，计算速度提升了340倍。
英文摘要：
The small-signal stability of a power system model with arbitrary loads is investigated, with a focus on locally constant power loads in lossless networks. A central element of the proposed analysis is the matrix H, which represents the partial derivatives of generator powers with respect to their relative angles. The local stability of any equilibrium point is determined by the properties of H if the loads consume locally constant power. Specifically, an equilibrium point is asymptotically stable if H is positive definite and unstable if H is full-rank and not positive definite, while several quantitative relationships between the eigenvalues of H and the system Jacobian matrix are also established. The main contribution is that loads are allowed to be arbitrarily located within the transmission network, thereby generalizing the existing H matrix stability criterion which is valid only if loads are located at the same buses as the generators. The advantage of the proposed criterion is demonstrated through case studies involving systems with up to 2869 buses. Accurate stability assessments are maintained, where alternative methods, such as the NRPS model, are found to be overly conservative. Additionally, a computational acceleration by a factor of 340 relative to Jacobian-based methods is achieved.
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