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Three-phase ideal active and reactive power sensor

**Library:**Simscape / Electrical / Sensors & Transducers

The Power Sensor (Three-Phase) block implements an ideal sensor for active and reactive power measurement in balanced or unbalanced three-phase branches.

For balanced branches, the block returns the correct value of the active and reactive power at all time instants. This is the preferred option for a load-flow analysis.

For unbalanced branches, to estimate the magnitude and phase, the block measures the phasors of the three voltages and currents independently by using a one-moving-period Fourier transform. For this reason, the output magnitude and phase are zero during the first period.

The equivalent balanced phase voltage, current, and apparent power are:

$$\begin{array}{l}{V}_{e}=\frac{1}{3}\sqrt{{V}_{ab}{}_{{}_{RMS}}^{2}+{V}_{bc}{}_{{}_{RMS}}^{2}+{V}_{ca}{}_{{}_{RMS}}^{2}}\\ {I}_{e}=\sqrt{\frac{{I}_{a}{}_{{}_{RMS}}^{2}+{I}_{b}{}_{{}_{RMS}}^{2}+{I}_{c}{}_{{}_{RMS}}^{2}+\rho {I}^{2}{}_{{n}_{RMS}}}{3}}\\ {S}_{e}=3{V}_{e}{I}_{e}\end{array}$$

where

*V*,_{abRMS}*V*, and_{bcRMS}*V*are the three phase-to-phase RMS voltages._{caRMS}*I*,_{aRMS}*I*, and_{bRMS}*I*are the RMS currents that flow through each of the three branches._{cRMS}*ρ*is the ratio of neutral conductor resistance over phase conductor resistance, specified by the Neutral conductor resistance divided by phase conductor resistance parameter.*I*is the RMS neutral current._{nRMS}

The active power is then defined by:

$$P={V}_{{a}_{RMS}}{I}_{{a}_{RMS}}\mathrm{cos}\left({\phi}_{{V}_{a}}-{\phi}_{{I}_{a}}\right)+{V}_{{b}_{RMS}}{I}_{{b}_{RMS}}\mathrm{cos}\left({\phi}_{{V}_{b}}-{\phi}_{{I}_{b}}\right)+{V}_{{c}_{RMS}}{I}_{{c}_{RMS}}\mathrm{cos}\left({\phi}_{{V}_{c}}-{\phi}_{{I}_{c}}\right),$$

where:

*V*,_{aRMS}*V*, and_{bRMS}*V*are the voltages of phase a, b, and c respectively._{cRMS}*φ*,_{Va}*φ*, and_{Vb}*φ*are the phase shifts of the_{Vc}*a*-phase,*b*-phase, and*c*-phase voltages.*φ*,_{Ia}*φ*, and_{Ib}*φ*are the phase shifts of the_{Ic}*a*-phase,*b*-phase, and*c*-phase currents.

To compute the reactive power, the block first calculates its absolute value and then finds the sign by looking at the sign of the phase shift:

$$\begin{array}{l}abs(Q)=\sqrt{{S}_{e}^{2}-{P}^{2}}\\ sign(Q)=sign(\phi )\\ Q=abs(Q)*sign(Q)\end{array}$$

where *φ =
φ _{V*} -
φ_{I*}*. The

If the block is in a network that is compatible with the frequency-time simulation mode, you can perform a load-flow analysis on the network. A load-flow analysis provides steady-state values that you can use to initialize a machine.

For more information, see Perform a Load-Flow Analysis Using Simscape Electrical and Frequency and Time Simulation Mode.

[1] Willems, Jacques, "The IEEE standard
1459: What and why?", *2010 IEEE International Conference on Applied
Measurements for Power Systems, Proceedings*: 41-46.

Current and Voltage Sensor (Three-Phase) | Line Voltage Sensor (Three-Phase) | Phase Voltage Sensor (Three-Phase) | Power Sensor