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# PLL

Determine frequency and fundamental component of signal phase angle

## Library

Simscape / Electrical / Specialized Power Systems / Control

• ## Description

The PLL block models a Phase Lock Loop (PLL) closed-loop control system, which tracks the frequency and phase of a sinusoidal signal by using an internal frequency oscillator. The control system adjusts the internal oscillator frequency to keep the phases difference to 0.

The figure shows the internal diagram of the PLL. The input signal is mixed with an internal oscillator signal. The DC component of the mixed signal (proportional to the phase difference between these two signals) is extracted with a variable frequency mean value. A Proportional-Integral-Derivative (PID) controller with an optional automatic gain control (AGC) keeps the phase difference to 0 by acting on a controlled oscillator. The PID output, corresponding to the angular velocity, is filtered and converted to the frequency, in hertz, which is used by the mean value.

## Parameters

Minimum frequency (Hz)

Specify the minimum expected frequency of the input signal. This parameter sets the buffer size of the Mean (Variable Frequency) block used inside the block to compute the mean value. Default is `45`.

Initial inputs [ Phase (degrees), Frequency (Hz) ]

Specify the initial phase and frequency of the input signal. Default is `[0, 60]`.

Regulator gains [ Kp, Ki, Kd ]

Specify the proportional, integral, and derivative gains of the internal PID controller. Use the gains to tune the PLL response time, overshoot, and steady-state error performances. Default is ```[180, 3200, 1]```.

Time constant for derivative action (s)

Specify the time constant for the first-order filter of the PID derivative block. Default is `1e-4`.

Maximum rate of change of frequency (Hz/s)

Specify the maximum positive and negative slope of the signal frequency. Default is `12`.

Filter cut-off frequency for frequency measurement (Hz)

Specify the second-order lowpass filter cut-off frequency. Default is `25`.

Sample time

Specify the sample time of the block, in seconds. Set to 0 to implement a continuous block. Default is `0`.

Enable automatic gain control

When this check box is selected, the PLL block optimizes its performances by scaling the PID regulator signal according to the input signal magnitude. Select this option when the input signal is not normalized. Default is selected.

## Inputs and Outputs

`In`

The normalized input signal, in pu.

`Freq`

The measured frequency, in hertz.

`wt`

Angle (rad) varying between 0 and 2*pi, synchronized on the zero-crossing (rising) of the fundamental of the input signal.

## Characteristics

 Sample Time Specified in the Sample Time parameter. Continuous when Sample Time = 0. Scalar Expansion No Dimensionalized No Zero-Crossing Detection Yes

## Examples

The `power_PLL` example shows the use of the PLL (3ph) and PLL blocks.

The PLL block is fed by a sinusoidal signal of 60 Hz, increasing to 61 Hz from 0.5 s to 1.5 s. Notice that the frequency reaches the new frequency in a short response time.

The PLL (3ph) block is fed by three-phase sinusoidal signals increasing from 60 Hz to 61 Hz between 0.5 and 1.5 seconds. The PLL (3ph) frequency reaches the new frequency faster than the PLL due to the additional phase information.

The model sample time is parameterized with the variable Ts (with a default value of 0). To discretize the PLL block, at the MATLAB® command prompt, enter

`Ts = 50e-6`

Introduced in R2013a

## Support

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