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Compute three-phase instantaneous active and reactive powers

Simscape / Electrical / Specialized Power Systems / Sensors and Measurements

The Power (dq0, Instantaneous) block computes the three-phase instantaneous active and reactive powers from a periodic set of three-phase voltages and currents expressed in the dq0 reference frame. These formulas perform the calculations:

$$\begin{array}{l}P=\frac{3}{2}\times \left({V}_{d}\cdot {I}_{d}+{V}_{q}\cdot {I}_{q}+2\cdot {V}_{0}\cdot {I}_{0}\right)\\ Q=\frac{3}{2}\times \left({V}_{q}\cdot {I}_{d}-{V}_{d}\cdot {I}_{q}\right)\end{array}$$

The inputs Vdq0 and Idq0 (direct axis, quadrature axis, and zero-sequence components) of the three-phase voltage and current are normally connected to the outputs of the abc-to-dqo Transformation block.

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.

`Vdq0`

The voltage signal, expressed in the dq0 reference frame.

`Idq0`

The current signal, expressed in the dq0 reference frame.

`P`

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

`Q`

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

The `power_ThreePhasePower`

model
compares the outputs of the block with the Power (Positive-Sequence)
block and the Power (3ph, Instantaneous) block. It shows that the
Power (dq0, 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.