# Constant Power Load (Three-Phase)

**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:

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

where:

*V*is the voltage peak magnitude._{pk}$${\phi}_{I}={\phi}_{V}-atan\left(\frac{Q}{P}\right)$$ 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:

$$R={V}^{2}{}_{line\text{\hspace{0.17em}}RM{S}_{min}}\frac{P}{{P}^{2}+{Q}^{2}}$$ is the constant resistance.

$$X={V}^{2}{}_{line\text{\hspace{0.17em}}RM{S}_{min}}\frac{Q}{{P}^{2}+{Q}^{2}}$$ is the constant reactance.

*V*is the_{line RMSmin}**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

## Parameters

## Extended Capabilities

## Version History

**Introduced in R2020b**