Constant Power Load (Three-Phase)

Three-phase constant power load

Since R2020b

• 

Libraries:
Simscape / Electrical / Passive

Description

The Constant Power Load (Three-Phase) block implements a constant power load for a three-phase supply.

The block outputs a nominal rated power as long as the voltage from the three-phase supply is equal to or greater than the value specified for the Minimum supply voltage (phase-to-phase RMS) parameter.

When the voltage from the three-phase supply drops below the value of Minimum supply voltage (phase-to-phase RMS), the load behavior changes and the block models a load with constant impedance.

Equations

When the voltage from the three-phase supply is greater than the value specified for the Minimum supply voltage (phase-to-phase RMS) parameter, the block acts in constant PQ mode.

The active and reactive power are defined by:

$$\begin{array}{l}P=\frac{3}{2}{V}_{pk}{I}_{pk}cos({\phi }_V-{\phi }_I)\\ Q=\frac{3}{2}{V}_{pk}{I}_{pk}\sin ({\phi }_V-{\phi }_I)\end{array}$$

where:

• V_pk is the voltage peak magnitude.

• $${\phi }_I={\phi }_V-atan\left(\frac{Q}{P}\right)$$ is the phase of the current.

• $$I_{pk}=\frac{2}{3}\frac{P}{V_{pk}cos\left({\phi }_V-{\phi }_I\right)}$$ is the current peak magnitude.

During the first period, the peak current is equal to 0 A.

When the voltage from the three-phase supply is less than or equal to the value specified for the Minimum supply voltage (phase-to-phase RMS) parameter, the block acts in constant Z mode.

The active and reactive power are defined by:

$$\begin{array}{l}P=\frac{3}{2}{V}_{pk}^2\frac{R}{R^2+X^2}\\ Q=\frac{3}{2}{V}_{pk}^2\frac{X}{R^2+X^2}\end{array}$$

where:

• $$R=V^2{}_{lineRM{S}_{min}}\frac{P}{P^2+Q^2}$$ is the constant resistance.

• $$X=V^2{}_{lineRM{S}_{min}}\frac{Q}{P^2+Q^2}$$ is the constant reactance.

• V_{line RMSmin} is the Minimum supply voltage (phase-to-phase RMS).

Load-Flow Analysis

If the block is in a network that is compatible with 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.

Faults

To model a fault in the Constant Power Load (Three-Phase) block, in the Faults section, click the Add fault hyperlink next to the fault that you want to model. In the Add Fault window, specify the fault properties. For more information about fault modeling, see Fault Behavior Modeling and Fault Triggering.

The Constant Power Load (Three-Phase) block allows you to model an electrical fault as an open circuit. The block can trigger fault events at a specific time.

Ports

Conserving

~ — Three-phase voltage

electrical

Composite three-phase port associated with the three-phase voltage.

Dependencies

To enable this port, set Electrical connection to Composite three-phase ports.

a — Phase A voltage

electrical

Expanded three-phase port associated with the phase A voltage.

Dependencies

To enable this port, set Electrical connection to Expanded three-phase ports.

b — Phase B voltage

electrical

Expanded three-phase port associated with the phase B voltage.

Dependencies

To enable this port, set Electrical connection to Expanded three-phase ports.

c — Phase C voltage

electrical

Expanded three-phase port associated with the phase C voltage.

Dependencies

To enable this port, set Electrical connection to Expanded three-phase ports.

Parameters

Main

Electrical connection — Electrical connection

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.

Rated electrical frequency — Rated electrical frequency

60 Hz (default) | positive scalar

Since R2023a

Rated electrical frequency.

Active power consumed — Active power consumed

1 kW (default) | scalar

Active power consumed by the block.

Reactive power consumed — Reactive power consumed

0 A*kV (default) | scalar

Reactive power consumed by the block.

Minimum supply voltage (phase-to-phase RMS) — Minimum supply voltage

100 V (default) | positive scalar

Minimum voltage, in phase-to-phase RMS, that the supply needs for the block to act as a constant power load.

Voltage time constant — Voltage dynamics time constant

0.01 s (default) | positive scalar

Since R2023a

Time constant associated with the transients of the terminal voltage measurement.

Initial supply voltage (phase-to-phase RMS) — Initial terminal voltage

200 V (default) | positive scalar

Since R2023a

Terminal voltage, in phase-to-phase RMS, at time zero.

Initial supply voltage angle — Terminal voltage angle of phase A at time zero

0 deg (default) | scalar

Since R2023a

Terminal voltage angle of phase A at time zero.

Parasitic conductance to electrical reference — Parasitic conductance to electrical reference

1e-6 S (default) | nonnegative scalar

Since R2023a

Parasitic conductance to electrical reference.

Faults

Open circuit fault — Option to add open circuit fault

Add fault (default)

Option to add an open-circuit fault in the Constant Power Load (Three-Phase) block.

To add a fault, click the Add fault hyperlink.

Open-circuit conductance — Open-circuit conductance

1e-4 S (default) | scalar

Conductance during the open-circuit state.

Dependencies

To enable this parameter, add a fault to the Constant Power Load (Three-Phase) block by clicking the Add fault hyperlink in the Open circuit fault parameter.

After you create the fault, you can change the properties in the Fault Inspector window. When you open a block that has a fault, the Open Fault Inspector hyperlink appears instead of the Add fault hyperlink. For an example that shows how to include faults, see Analyze a DC Armature Winding Fault.

Trigger fault at time — Time before entering faulted state

0 s (default) | nonnegative scalar

Simulation time at which the block enters the faulted state.

Dependencies

To enable this parameter, in the Fault Inspector window, set Trigger Type to Timed.

This parameter appears in the Trigger section of the Fault Inspector window. For more information, see Set Fault Triggers.

Extended Capabilities

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

Version History

Introduced in R2020b

R2023a: Improved support for inductive nodes

Prior to R2023a, to connect the Constant Power Load (Three-Phase) block to an inductive node, you had to provide a large parasitic resistance. From R2023a, you can connect this block to an inductive node by specifying the Rated electrical frequency, Voltage time constant, Initial supply voltage (phase-to-phase RMS), Initial supply voltage angle, and Parasitic conductance to the electrical reference parameters. If your model saved in an earlier release contains this block you must set appropriate values to these parameters.

Additionally, the Modeling option parameter of the block has been renamed to Electrical connection and moved to the Main section.