基于低通滤波器的标幺化锁相环同步稳定性分析

Analysis of Synchronization Stability of the Normalization PLL Based on Low-pass Filter

为了保持锁相环(phase locked loop,PLL)的带宽不受到并网同步点电压的影响,锁相环通常都会将q轴电压除以d轴电压进行标幺化,称之为标幺化锁相环。如果不对标幺化锁相环的d轴电压进行低通滤波,在大于90°的相位扰动下锁相环会失去相位跟踪能力。加入低通滤波器(low pass filter,LPF)后可以改善锁相环的同步能力,于是首次建立考虑低通滤波器的标幺化锁相环的三阶非线性大信号模型,通过相平面法分析带有LPF的标幺化锁相环在不同相位扰动下的相位跟踪能力。理论分析表明LPF的存在有利于提升大部分相位扰动下锁相环的锁相能力,即当相位跳变大于90°的大部分情况下,锁相环依然能够准确跟踪电网电压;而且可以证明锁相能力随着LPF带宽的降低而增加,但在某些极端相位扰动下,LPF的存在依然不能避免锁相环失去同步能力的情况。因此,带LPF环节的标幺化锁相环也需谨慎使用,尤其在同步稳定性要求高的场合下应避免使用。最后通过仿真和实验验证了所推导的数学模型和所得结论的准确性。

In order to keep the bandwidth of phase locked loop(PLL)from being affected by the voltage at the synchronous point connected to the grid,the q-axis voltage is usually divided by the d-axis voltage in PLL for normalization,which is called the normalization PLL.If the d-axis voltage is not filtered by low-pass filter(LPF),the normalization PLL will lose the phase tracking ability under the phase disturbance greater than 90°.The synchronization ability of PLL can be improved by adding LPF.Therefore,the third-order nonlinear large signal model of the normalization PLL considering LPF is established for the first time in this paper,and the phase tracking ability of the normalization PLL with LPF under different phase disturbances is analyzed by phase plane method.The theoretical analysis shows that the existence of LPF is beneficial to improvements in the phase tracking ability of PLL under most severe conditions,that is,when the phase jump is greater than 90°,PLL can still follow the grid voltage accurately.Moreover,it can be proved that the phase tracking ability increases with the decrease of LPF bandwidth;however,under some extreme phase disturbances,the existence of LPF still cannot avoid the loss of synchronization capability of PLL.Therefore,the normalization PLL with LPF should also be used with caution,especially in the case of requirement of precise synchronization stability.Finally,the accuracy of the derived mathematical model and the above conclusions are verified by simulations and experiments.