A single-phase amplitude-phase-locked loop(1MPLL) system based on objective function optimization ideasis designed and the design method of system parameters is discussed in detail. In order to improve the harmonic suppression capability

1MPLL constructs the objective function based on integration of system deviation in the most recent time interval

the steepest descent direction is analyzed using the gradient descent method. And the nonlinear state equation of phase-locked loop system is derived to estimate the properties of the input signal. In order to carry out system performance analysis and parameter design

the system nonlinear state equation is linearized at the equilibrium point and the system parameters are designed with the root locus theory. The properties of the input signal are estimated quickly and accurately by IMPLL for a variety of power quality problems (such as amplitude mutation

frequency fluctuation

phase change

especially harmonic pollution)

providing effective and reliable baseline for the detection and control of grid power electronic equipment. Simulation and experiment results verify the correctness of the system design and good system performance.