Power Sensor (Three-Phase)

Three-phase ideal active and reactive power sensor

Since R2020b

• 

Libraries:
Simscape / Electrical / Sensors & Transducers

Description

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.

Unbalanced Branches Equations

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

$$\begin{array}{l}{V}_e=\frac{1}{3}\sqrt{V_{ab}{}_{{}_{RMS}}^2+V_{bc}{}_{{}_{RMS}}^2+V_{ca}{}_{{}_{RMS}}^2}\\ I_e=\sqrt{\frac{I_a{}_{{}_{RMS}}^2+I_b{}_{{}_{RMS}}^2+I_c{}_{{}_{RMS}}^2+\rho I^2{}_{n_{RMS}}}{3}}\\ S_e=3V_e{I}_e\end{array}$$

where

• V_abRMS, V_bcRMS, and V_caRMS are the three phase-to-phase RMS voltages.

• I_aRMS, I_bRMS, and I_cRMS are the RMS currents that flow through each of the three branches.

• 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_nRMS is the RMS neutral current.

The active power is then defined by:

$$P=V_{a_{RMS}}{I}_{a_{RMS}}\cos \left({\phi }_{V_a}-{\phi }_{I_a}\right)+V_{b_{RMS}}{I}_{b_{RMS}}\cos \left({\phi }_{V_b}-{\phi }_{I_b}\right)+V_{c_{RMS}}{I}_{c_{RMS}}\cos \left({\phi }_{V_c}-{\phi }_{I_c}\right),$$

where:

• V_aRMS, V_bRMS, and V_cRMS are the voltages of phase a, b, and c respectively.

• φ_Va, φ_Vb, and φ_Vc are the phase shifts of the a-phase, b-phase, and c-phase voltages.

• φ_Ia, φ_Ib, and φ_Ic are the phase shifts of the 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 * symbol denotes the central phase in the [-π,π] range.

Load-Flow Analysis

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.

Ports

Conserving

~1 — Three-phase port

electrical

Expandable three-phase electrical port.

~2 — Three-phase port

electrical

Expandable three-phase electrical port.

Output

P — Active power

physical

Physical signal port associated with the active power measurements.

Q — Reactive power

physical

Physical signal port associated with the reactive power measurements.

Parameters

Modeling option — Whether to model composite or expanded three-phase ports

Composite three-phase ports (default) | Expanded three-phase ports

Whether to model composite or expanded three-phase ports.

Composite three-phase ports represent three individual electrical conserving ports with a single block port. You can use composite three-phase ports to build models that correspond to single-line diagrams of three-phase electrical systems.

Expanded three-phase ports represent the individual phases of a three-phase system using three separate electrical conserving ports.

Load type — Load type

Balanced (default) | Unbalanced

Type of load. Select Balanced if the three-phase branches are balanced, Unbalanced if the branches are not balanced.

Rated frequency — Rated frequency

60 Hz (default) | scalar

Rated frequency.

Dependencies

To enable this parameter, set Load Type to Unbalanced.

Downstream configuration — Downstream configuration

Without neutral (default) | With neutral

Whether the downstream configuration is with or without neutral.

Dependencies

To enable this parameter, set Load Type to Unbalanced.

Neutral conductor resistance divided by phase conductor resistance — Ratio of neutral conductor resistance over phase conductor resistance

1 (default) | scalar

Ratio of neutral conductor resistance over phase conductor resistance, $$\frac{R_{neutral}}{R_{phase}}.$$.

Dependencies

To enable this parameter, set Downstream configuration to With neutral.

References

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

Extended Capabilities

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

Version History

Introduced in R2020b