All digital phase-locked loop optimized design based on lyapunov function

In this paper, the principle and nonlinear dynamic model of the digital phase-locked loop (PLL) based on vector transformation are demonstrated under the condition of distorted three-phase. Then the design method of three-phase digital PLL based on Lyapunov function is proposed, and the designed PLL possesses high stability and excellent phase tracking capability. Furthermore, the loop filter and voltage controlled oscillator (VCO) with auto-reset function are discretized separately, solving the problem of finite word length of processors during digitization. PLL errors are computed and analyzed under distortion conditions such as phase imbalance, harmonics, offset. Instead of the traditional loop filter, a proportional-integral (PI) controller is used to improve the distortion elimination capability and the response tracking rate of three-phase digital PLLs. The three-phase digital PLL is realized based on a digital signal processor (DSP) platform and is applied to the power factor control of 6kW inverters. Simulations and experiments validate the theoretical analysis.