# Fundamental (PLL-Driven)

Compute fundamental value of signal

## Library

Control and Measurements/Measurements

## Description

The Fundamental (PLL-Driven) block computes the fundamental value of the input 3 over a running window of one cycle of fundamental frequency given by input 1. The reference frame required for the computation is given by the input 2.

Based on the Fourier analysis of a periodic signal, the fundamental value of a signal f(t) can be expressed as

The magnitude and phase of the fundamental is calculated by

To resolve these equations, the block uses the input 1 (Freq) for f0 and input 2 (wt) for ω0t. These two input signals are normally connected to the outputs of a PLL block.

As this block uses a running average window, one cycle of simulation must complete before the outputs give the correct magnitude and angle. For the first cycle of simulation, the outputs are held to the values specified by the initial input parameter.

## Dialog Box and Parameters

Initial frequency (Hz)

Specify the frequency of the first cycle of simulation.

Minimum frequency (Hz)

Specify the minimum frequency value that sets the buffer size of the Variable Time Delay block used inside the block to compute the fundamental value.

Initial input [ Mag, Phase-relative-to-PLL (degrees) ]

Specify the initial magnitude and phase in degrees of the input signal.

Sample time

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

## Inputs and Outputs

`Freq`

Fundamental frequency (Hz) required by the computation. This input is normally connected to the output Freq of a PLL block.

`wt`

Angle of the reference frame (rad/s) required for the computation. This input is normally connected to the output wt of a PLL block.

`In`

Connects to the signal to be analyzed. Typical input signals are voltages or currents measured by the Current Measurement or Voltage Measurement block.

|u|`Magnitude`

Returns the magnitude of the fundamental in the same unit as the input signal.

$\angle \text{u}$`Phase`

Returns the phase of the fundamental, in degrees, relative to the reference frame wt (input 2).

## Characteristics

 Sample Time Specified in the Sample Time parameterContinuous if Sample Time = 0 Scalar Expansion Yes, of the parameters Dimensionalized Yes, for Input 3 (In)

## Example

The `power_FundamentalPLLDriven` model compares the Fourier block (with a specified fundamental frequency of 60 Hz) output to the Fundamental (PLL-Driven) block output. The PLL-Driven block outputs accurate magnitude and phase even if the fundamental frequency of the input signal varies during the simulation.

The model sample time is parameterized by the Ts variable set to a default value of 50e-6 s. Set Ts to 0 in the command window to simulate the model in continuous mode.