# Constant Power Load (Three-Phase)

Three-phase constant power load

**Library:**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 behaviour 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.

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:

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

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

## Limitations

If you connect this block to an inductive node or a current source, you must provide a large parasitic.

## Ports

### Conserving

## Parameters

## Extended Capabilities

## Version History

**Introduced in R2020b**