# Power (3ph, Instantaneous)

Compute three-phase instantaneous active and reactive powers

Libraries:
Simscape / Electrical / Specialized Power Systems / Sensors and 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.

### Examples

The `power_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.

## Ports

### Input

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Three-phase voltage signal.

Three-phase current signal.

### Output

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Three-phase instantaneous active power P, in watts.

Three-phase instantaneous reactive power Q, in vars.

## Version History

Introduced in R2013a