# Positive-Sequence (PLL-Driven)

Compute positive-sequence component of three-phase signal at fundamental frequency

## Library

Simscape / Electrical / Specialized Power Systems / Sensors and Measurements

## Description

The Positive-Sequence (PLL-Driven) block computes the positive-sequence component (magnitude and phase) of the input 3 signal over a running window of one cycle of the fundamental frequency given by input 1. The reference frame required for the computation is given by the input 2. The first two inputs are normally connected to a PLL block.

The positive-sequence component of a three-phase signal (V_{1} or
current I_{1}) is computed as

$$\begin{array}{l}{V}_{1}=\frac{1}{3}\left({V}_{a}+a\cdot {V}_{b}+{a}^{2}\cdot {V}_{c}\right)\\ {V}_{a},{V}_{b},{V}_{c}=\text{threevoltagephasorsatthefundamentalfrequency}\\ a={e}^{j2\pi /3}=1\angle 120\xb0\text{complexoperator}\end{array}$$

A Fourier analysis over a sliding window of one cycle of the fundamental frequency (input 1) is first applied to the three input signals. The block evaluates the phasor values at the fundamental. Then the transformation is applied to obtain the positive sequence.

As the block uses a running average window to perform the Fourier
analysis, one cycle of simulation must complete before the outputs
give the correct magnitude and angle. For example, the block response
to a step change of V_{1} is a one-cycle ramp.
For the first cycle of simulation, the output is held constant to
the values specified by the initial input parameters.

## Parameters

**Initial frequency (Hz)**Specify the frequency of the first cycle of simulation. Default is

`60`

.**Minimum frequency (Hz)**The minimum frequency value determines the buffer size of the Variable Time Delay block used inside the block to compute the phasors. Default is

`45`

.**Initial input (positive component) [ Mag, Phase-relative-to-PLL (degrees) ]**Specify the initial positive-sequence magnitude and phase (relative to the PLL phase), in degrees, of the input signals. Default is

`[1, 0]`

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

`0`

.

## Inputs and Outputs

`Freq`

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

`wt`

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

`abc`

The vectorized signal of the three [a b c] sinusoidal signals. Typical input signals are voltages or currents measured by Current Measurement or Voltage Measurement blocks.

- |u|
`Magnitude`

Outputs the magnitude of the positive-sequence component in the same unit as the input signal.

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

Outputs the phase of the positive-sequence component, 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 | No |

Dimensionalized | No |

## Examples

The `power_PositiveSequencePLLDriven`

model
computes the positive-sequence component of a three-phase signal containing
harmonics. It shows that the 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.

## Version History

**Introduced in R2013a**