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This work presents the design and analysis of an enhanced phase-locked loop (EPLL) for single-phase power systems. This paper examines two methods for developing an EPLL: gradient-flow optimization and Lyapunov theory. The derived nonlinear differential equations of EPLL are analyzed for stability using dynamic system theory. Computer simulations show that the proposed EPLL structure is highly efficient at extracting amplitudes, phases, and frequencies that match actual values, even in the presence of harmonics.
Abrar et al. (Thu,) studied this question.