# Power (PLL-Driven, Positive-Sequence)

Compute positive-sequence active and reactive powers

## Library

Simscape / Electrical / Specialized Power Systems / Sensors and Measurements

## Description

The Power (PLL-Driven, Positive-Sequence) block computes the positive-sequence active power P (in watts) and reactive power Q (in vars) of a periodic set of three-phase voltages and currents. To perform this computation, the block first computes the positive sequence of the input voltages and currents with a running window over 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 the outputs of a PLL block.

These formulas are then evaluated:

`$\begin{array}{c}P=3×\frac{|{V}_{1}|}{\sqrt{2}}×\frac{|{I}_{1}|}{\sqrt{2}}×\mathrm{cos}\left(\phi \right)\\ Q=3×\frac{|{V}_{1}|}{\sqrt{2}}×\frac{|{I}_{1}|}{\sqrt{2}}×\mathrm{sin}\left(\phi \right)\\ \phi =\angle {V}_{1}-\angle {I}_{1}\end{array}$`

V1 is the positive-sequence component of input Vabc. I1 is the positive-sequence component of input Iabc.

With these formulas, a current flowing into an RL circuit produces a positive P and a positive Q.

As this block uses a running average window, one cycle of simulation must complete before the outputs give the correct value. For the first cycle of simulation, the output is held constant using the values specified by the Voltage initial input and Current initial input parameters.

## Parameters

Initial frequency (Hz)

Specify the frequency of the first cycle of simulation. Default is `60`.

Minimum frequency (Hz)

Specify the minimum frequency value to determine the buffer size of the Variable Time Delay block used by the block to compute the phasors. Default is `45`.

Voltage initial input [ Mag, Phase (degrees) ]

Specify the initial positive-sequence magnitude and phase (relative to the PLL phase), in degrees, of the voltage signals. Default is ```[1, 0]```.

Current initial input [ Mag, Phase (degrees) ]

Specify the initial positive-sequence magnitude and phase (relative to the PLL phase), in degrees, of the current 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 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.

`Vabc`

The vectorized signal of the three [a b c ] voltage sinusoidal signals. Typical input signals are voltages measured by the Three-Phase V-I Measurement block.

`Iabc`

The vectorized signal of the three [a b c ] current sinusoidal signals. Typical input signals are currents measured by the Three-Phase V-I Measurement block.

`P`

Positive-sequence active power (watts)

`Q`

Positive-sequence reactive power (vars)

## Characteristics

 Sample Time Specified in the Sample Time parameter Continuous if Sample Time = 0 Scalar Expansion No Dimensionalized No

## Examples

The `power_PowerPLLDrivenPositiveSequence` model shows how the block evaluates the positive-sequence active and reactive powers of a voltage source connected to a three-phase load. It shows that the block outputs accurate values for P and Q even if the fundamental frequency of the voltage supply (containing harmonics) 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 and change the Simulation type parameter of the Powergui block to `Continuous` to simulate the model in continuous mode.

Introduced in R2013a