AI 中文总结
该研究基于艾哈迈迪 - 乔杜里 - 张高阶牛顿框架设计新型高阶增强型锁相环，通过坐标优化策略应用于EPLL，经相图分析，其消除虚假平衡点和鞍点，扩大吸引域，具有理想收敛特性。
AI 中文摘要
增强型锁相环（EPLL）广泛用于电力系统中估计正弦电压的幅度、相位和频率。现有EPLL公式主要源自一阶或二阶优化方法，可能存在收敛慢、鞍点吸引或不良振荡行为。本文提出基于最近提出的艾哈迈迪 - 乔杜里 - 张（ACZ）高阶牛顿框架的新型高阶EPLL。因ACZ方法最初用于标量离散时间优化，故为自适应系统制定连续时间高阶牛顿流。通过坐标优化策略将所得框架应用于EPLL，高阶牛顿流仅用于相位更新，幅度更新保留经典形式，因其成本函数恰好是二次的。通过相图分析所提出的自治系统，并与标准、牛顿和改进的EPLL公式进行比较。自治模型的相图分析表明，所提出的流消除了自治牛顿EPLL中存在的虚假平衡点和鞍点，大幅扩大了与期望平衡点相关的吸引域，并与改进的EPLL具有一些理想的收敛特性。
英文摘要
The enhanced phase-locked loop (EPLL) is widely used in power systems to estimate the amplitude, phase, and frequency of sinusoidal voltages. Existing EPLL formulations are primarily derived from first- or second-order optimization methods, which may exhibit slow convergence, saddle-point attraction, or undesired oscillatory behavior. This paper presents a new higher-order EPLL based on the recently proposed Ahmadi-Chaudhry-Zhang (ACZ) higher-order Newton framework. Since the ACZ method was originally developed for scalar discrete-time optimization, a continuous-time higher-order Newton flow is formulated for adaptive systems. The resulting framework is then applied to the EPLL through a coordinate optimization strategy, whereby the higher-order Newton flow is applied only to the phase update, while the amplitude update retains its classical form because its cost function is exactly quadratic. The proposed autonomous system is analyzed through phase portraits and compared with the standard, Newton, and modified EPLL formulations. Phase-portrait analysis of the autonomous model shows that the proposed flow eliminates the spurious equilibria and saddle points present in the autonomous Newton EPLL, substantially enlarges the basin of attraction associated with the desired equilibrium, and shares several desirable convergence characteristics with the modified EPLL.
