并网逆变器数字锁相环的数学物理本质分析

Mathematical and Physical Fundaments of Digital Phase-Locked Loop for Grid-Connected Inverters

锁相环是并网逆变器与电网保持同步的关键环节,其高性能稳定运行是可再生能源接入电网的重要保障。从非线性动力学模型的角度揭示锁相环的数学本质,从虚拟同步电机的角度揭示锁相环的物理本质,采用李雅普诺夫能量函数分析锁相环的稳定条件,并分析电网电压不对称、低频谐波和直流偏置对锁相环的影响机理。此外,以一种基于隐式比例积分控制的锁相环结构为例,研究非线性动力学模型在探索新型锁相环结构中的应用。最后,考虑电网电压的频率阶跃、相位跳变、不平衡跳变、低频谐波跳变等扰动,利用实验结果对比研究锁相环的输出特性,为锁相环的研究提供了一条新的思路和方法。

Phase-locked loop（PLL） is one of the key elements of grid-connected inverter for renewable energy integration.Its performance and stability are important to guarantee the increasing penetration of renewable energy resources in utility.In this paper,the mathematical fundament of PLL is indicated by using nonlinear dynamic model.Meanwhile,the physical fundament of PLL is displayed by using the synchronous generator model.Lyapunov energy function is utilized to identify the stability of PLL.Based on the proposed model,the affecting mechanisms of low-frequency harmonic,unbalanced,and dc-bias voltage on PLL are achieved.Besides,taking an implicit proportional-integral based PLL into account,this paper also studies how the nonlinear mathematical model can be used to explore new PLL structure.Finally,experimental results are presented to study the PLLs in frequency variation,phase stepping,unbalanced,and distorted utility voltage conditions.