PLL

Symbol

Description

Single-phase Phase-Locked Loop (PLL)

Description

The single-phase Phase Locked Loop (PLL) proposes an estimation of the input signal frequency, signal amplitude and the phase-angle.

This block implements an Enhanced PLL described in Teoderescu et al.[1]

As shown below, the performance of the basic PLL implementation is enhanced with an Adaptative Noise Canceling (ANC) system which is an Adaptative Notch Filter (ANF).

Shematic of the Enhanced PLL

The output of the ANF becomes equal to zero as the frequency and phase-angle of the reference signal generated by the VCO, $x = cos(θ′)$ , match those of the input signal $v$ . As a result, signal oscillations at the output of the multiplier PD are completely cancelled out and the input signal phase-angle is accurately estimated by the basic PLL structure.

Controller Design

Two approaches to set the gains of the phase detector ( $K_{i_{pd}}$ ) and of the loop filter which is a PI controller ( $K_{p_{lf}}$ and $K_{i_{lf}}$ ).

Auto approach: the parameters are automatically calculated [2] to get a settling time (ts) of approximately $3 / f_0$ where $f_0$ is the frequency defined by the user.

ts = 3 / fo;         // Settling Time
xsi = 1 / sqrt(2);   // Damping factor
Kp_lf = 9.2 / ts;
Ti_lf = ts * xsi^2 / 2.3;
Ki_lf = Kp_lf / Ti_lf;
Ki_pd = Kp_lf;

Advanced approach: $K_{i_{pd}}$ , $K_{p_{lf}}$ and $K_{i_{lf}}$ are defined by the user.

Info

The input signal is normalized in the PLL block so the parameters are not required to be scaled.

Important

The unit for phase-angle is the radian (rad) and the unit for the frequency is the Hertz (Hz).

References

[1]: R. Teodorescu, M. Liserre, and P. Rodriguez, "Chapter 4 – Grid Synchronization in Single-Phase Power Converters" in Grid Converters for Photovoltaic and Wind Power Systems, John Wiley and Sons, 2011. [2]: Y. Yang, K. Zhou Chapter 4 - Modeling and Control of Single-Phase AC/DC Converters in Control of Power Electronic Converters and Systems Vol 1, Science Direct, 2018.

Library

Control > Math

Pins

Name	Description
In	Input signal
Freq	Estimated Frequency [Hz]
Angle	Estimated Phase Angle [rad]
Mag	Estimated Magnitude

Parameters

Name	Description
SamplingTime	-none or 0: No sampling. The system will be solved in the Newton loop (default). -auto: Inherit the sampling time of its source device. -Sampling Period: defined in seconds.