发表机构
ETH Zurich; University of Sydney; University of Bath; Imperial College London; Nanyang Technological University（苏黎世联邦理工学院; 悉尼大学; 巴斯大学; 帝国理工学院; 南洋理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出利用凸半定规划（SDP）系统性搜索分散式稳定性证书的最优多乘子，针对即插即用加性节点导纳证书给出算法，在IEEE 39节点系统上验证了比分段常数多乘子更广的下垂增益认证区域。
AI 中文摘要
分散式稳定性证书允许基于逆变器的资源接入电网，而无需重复进行全系统的小信号研究。无源性提供了此类证书，但实际的构网型（GFM）控制在低频时会违反无源性，其推广形式——变换矩阵、扩展无源性指标、环路移位和增益-相位条件——依赖于解析构造或启发式选择的多乘子。所有这些证书在每个频率上都是关于其多乘子的线性矩阵不等式，因此搜索最不保守的多乘子是一个凸半定规划（SDP），具有全局最优解和明确的不可行性判定。本文演示了如何将SDP应用于搜索文献中提出的几种分散式方法的最优多乘子。然后，通过提出一种针对完全即插即用的加性节点导纳证书的系统性搜索算法来说明该方法，该证书不需要组装的网络模型，并且适用于任意互连。仅需采样的频率响应，使得搜索与黑盒模型和阻抗扫描兼容。切比雪夫参数化结合自适应频率分割提供了分段多项式多乘子，无需手动分区。在带有十个下垂控制GFM的IEEE 39节点系统上，该多乘子比分段常数多乘子认证了更大的下垂增益区域，这一点通过随机逆变器布置的仿真得到证实。
英文摘要
Decentralized stability certificates allow inverter-based resources to be connected to a grid without repeating a system-wide small-signal study. Passivity provides such certificates but is violated by practical grid-forming (GFM) controls at low frequency, and its generalizations---transformation matrices, extended passivity indices, loop shifting, and gain--phase conditions---rely on multipliers that are constructed analytically or chosen heuristically. All of these certificates are linear matrix inequalities in their multipliers at every frequency, so the search for the least conservative multiplier is a convex semidefinite program (SDP) with a global optimum and a definite infeasibility verdict. This paper demonstrates how SDP can be applied to searching for optimal multipliers for some decentralized methods proposed in the literature. Then it illustrates the methodology by presenting a systematic search algorithm for the fully plug-and-play additive nodal-admittance certificate, which requires no assembled network model and holds for arbitrary interconnections. Only sampled frequency responses are needed, making the search compatible with black-box models and impedance scans. Chebyshev parameterization together with adaptive frequency splitting provides a piecewise-polynomial multiplier without manual partitioning. On the IEEE 39-bus system with ten droop-controlled GFMs, this multiplier certifies a larger region of droop gains than piecewise-constant multipliers, as confirmed by simulation of random inverter placements.
