Design and Analysis of a Higher-Order Enhanced Phase-Locked Loop via the Ahmadi-Chaudhry-Zhang Newton Framework
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.