Power Measurement (Three-Phase, Instantaneous)

Calculate three-phase real and reactive instantaneous power

Since R2026a

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Libraries:
Simscape / Electrical / Control / Measurements

Description

The Power Measurement (Three-Phase, Instantaneous) block measures the real and reactive instantaneous power of an element in a three-phase network. You can calculate the real and reactive instantaneous power in the abc, alpha-beta-zero (αβ0), or direct-quadrature-zero (dq0) reference frame.

To measure single-phase power, use the Power Measurement block instead.

Equations

To use the abc reference frame, set Reference frame to abc. When you use this frame, the a, b, and c axes are fixed on the same plane with a 2π/3 displacement between any two axes. The block computes the instantaneous power in the abc reference frame by using these equations:

$$\begin{array}{l}P=\left[\begin{array}{ccc}{v}_a& v_b& v_c\end{array}\right]\left[\begin{array}{c}{i}_a\\ i_b\\ i_c\end{array}\right]\\ Q=\frac{1}{\sqrt{3}}\left[\begin{array}{ccc}{v}_b-v_c& v_c-v_a& v_a-v_b\end{array}\right]\left[\begin{array}{c}{i}_a\\ i_b\\ i_c\end{array}\right]\end{array}$$

To use the αβ0 reference frame, set Reference frame to Alpha-beta-zero. When you use this frame, the block computes the instantaneous power by using the power-invariant Clarke transform:

$$\begin{array}{l}P=\left[\begin{array}{ccc}{v}_{\alpha }& v_{\beta }& v_0\end{array}\right]\left[\begin{array}{c}{i}_{\alpha }\\ i_{\beta }\\ i_0\end{array}\right]\\ Q=\left[\begin{array}{cc}{v}_{\beta }& -v_{\alpha }\end{array}\right]\left[\begin{array}{c}{i}_{\alpha }\\ i_{\beta }\end{array}\right]\end{array}$$

To use the dq0 reference frame, set Reference frame to Direct-quadrature-zero. When you use this frame, the block computes the instantaneous power by using the Park transform:

$$\begin{array}{l}P=\frac{3}{2}\left[\begin{array}{ccc}{v}_d& v_q& v_0\end{array}\right]\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 2\end{array}\right]\left[\begin{array}{c}{i}_d\\ i_q\\ i_0\end{array}\right]\\ Q=\frac{3}{2}\left[\begin{array}{cc}{v}_q& -v_d\end{array}\right]\left[\begin{array}{c}{i}_d\\ i_q\end{array}\right]\end{array}$$

Ports

Input

V — Voltage in selected reference frame, V

vector of three elements

Three-phase voltage across the element, in volts. The block uses this voltage to measure the instantaneous power.

I — Current in selected reference frame, A

vector of three elements

Three-phase current across the element, in amperes. The block uses this current to measure the instantaneous power.

Output

P — Instantaneous real power, W

scalar

Instantaneous real power, in watts.

Q — Instantaneous reactive power, var

scalar

Instantaneous reactive power, in volt-ampere reactive (var).

Parameters

To edit block parameters interactively, use the Property Inspector. From the Simulink^® Toolstrip, on the Simulation tab, in the Prepare gallery, select Property Inspector.

Reference frame — Reference frame for power measurement

abc (default) | Alpha-beta-zero | Direct-quadrature-zero

Frame to use as the reference frame for the power measurement.

References

[1] Akagi, Hirofumi, Yoshihira Kanazawa, and Akira Nabae. “Instantaneous Reactive Power Compensators Comprising Switching Devices without Energy Storage Components.” IEEE Transactions on Industry Applications IA-20, no. 3 (1984): 625–30. https://doi.org/10.1109/TIA.1984.4504460

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2026a