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# Power (3ph, Instantaneous)

Compute three-phase instantaneous active and reactive powers

## Library

Control and Measurements/Measurements

## Description

The Power (3ph, Instantaneous) block computes the three-phase instantaneous active power P (in watts) and reactive power Q (in vars) associated with a periodic set of three-phase voltages and currents. These formulas are used to perform the calculations:

$\begin{array}{l}P={V}_{a}\cdot {I}_{a}+{V}_{b}\cdot {I}_{b}+{V}_{c}\cdot {I}_{c}\\ Q=\frac{1}{\sqrt{3}}\left[\left({V}_{b}-{V}_{c}\right)\cdot {I}_{a}+\left({V}_{c}-{V}_{a}\right)\cdot {I}_{b}+\left({V}_{a}-{V}_{b}\right)\cdot {I}_{c}\right]\end{array}$

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

The computed instantaneous reactive power is accurate only for balanced and harmonic-free three-phase voltages and currents.

## Dialog Box and Parameters

The block has no parameters.

## Inputs and Outputs

Vabc

The three-phase voltage signal.

Iabc

The three-phase current signal.

P

The three-phase instantaneous active power P, in watts.

Q

The three-phase instantaneous reactive power Q, in vars.

## Example

The power_ThreePhasePowerpower_ThreePhasePower model compares the outputs of the block with the Power (Positive-Sequence) block and the Power (dq0, Instantaneous) block. It shows that the Power (3ph, Instantaneous) block gives accurate results when the voltages and currents are balanced and harmonic free. When the voltage supply becomes unbalanced, the P output exhibits a ripple, and an error appears on the Q output.

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.