# Average-Value Inverter (Three-Phase)

Average-value DC Voltage to three-phase AC voltage converter with fixed power loss

**Library:**Simscape / Electrical / Semiconductors & Converters / Converters

## Description

The Average-Value Inverter (Three-Phase) block models an average-value, full-wave inverter. It converts DC voltage to three-phase AC voltages and converts three-phase AC power demand to DC power demand. The corresponding DC power demand is equal to the sum of the fixed power loss and the AC power demand.

You can use the Average-Value Inverter (Three-Phase) block only as a full-wave inverter. It behaves as a DC-voltage-controlled AC voltage source. The ratio you specify determines the ratio between the DC voltage and the AC voltage.

The figure shows the equivalent circuit for the inverter as a full-wave inverter. The Average-Value Inverter (Three-Phase) block does not yield the harmonics that are typically associated with the detailed representation, however, because it performs an average-value power conversion.

### Electrical Defining Equations

The voltages are defined by

$${v}_{DC}={v}_{p}-{v}_{n},$$

$${v}_{ref}=\frac{{v}_{p}+{v}_{n}}{2},$$

$${v}_{RMS}={v}_{ratio}{v}_{DC},$$

$${V}_{0}=\frac{\sqrt{2}}{\sqrt{3}}{V}_{RMS},$$

$${v}_{a}={V}_{0}\mathrm{sin}(2\pi ft+\phi )+{v}_{ref},$$

$${v}_{b}={V}_{0}\mathrm{sin}(2\pi ft+\phi -{120}^{\circ})+{v}_{ref},$$

and

$${v}_{c}={V}_{0}\mathrm{sin}(2\pi ft+\phi +{120}^{\circ})+{v}_{ref},$$

where:

*v*and_{p}*v*are the voltages at the positive and negative terminals of the inverter._{n}*v*is the voltage difference between the positive and negative terminals of the inverter._{DC}*v*is the DC offset._{ref}*V*is the ratio of rated AC voltage to rated DC voltage for the inverter. See the_{ratio}**Ratio of rated AC voltage to rated DC voltage**parameter in Parameters for the*V*values for common inverter control modes._{ratio}*V*is the RMS AC line-line voltage._{RMS}*V*is the peak phase voltage._{0}*f*is the frequency.*t*is the time.*φ*is the phase shift.*v*,_{a}*v*,_{b}*v*are the respective AC phase voltages._{c}

The power, resistance, and currents are defined by

$${P}_{AC}=-{v}_{a}{i}_{a}-{v}_{b}{i}_{b}-{v}_{c}{i}_{c},$$

$${R}_{DC}=\frac{{v}_{DC}^{2}}{{P}_{AC}+{P}_{fixed}},$$

and

$$i=\frac{{v}_{DC}}{{R}_{DC}},$$

where:

*i*,_{a}*i*, and_{b}*i*are the respective AC phase currents flowing into the inverter._{c}*P*is the power output on the AC side._{AC}*P*has a minimum limit of_{AC}`0`

W.*P*is the fixed power loss that you specify on the block._{fixed}*R*is the resistance on the DC side._{DC}*i*is the current flowing from the positive to the negative terminals of the inverter.

The inverter starts to create an AC voltage, that is turns on, when the DC supply
voltage is above the value that you specify for **DC voltage for turn
on** parameter. It stops inverting, that is turns off, when the DC
supply voltage falls below the value that you specify for **DC voltage for
turn off** parameter. When the inverter turns off, the block sets the
output AC current to zero.

## Ports

### Conserving

## Parameters

## References

[1] Rashid, M. H. *Pulse-Width-Modulation
Inverters.* Upper Saddle River, NJ: Prentice-Hall, 2004, pp.
237–248.

[2] Krause, P. C., O. Wasynczuk, and S. D. Sudhoff.
*Analysis of Electric Machinery and Drive Systems*. Piscataway,
NJ: IEEE Press, 2002.

[3] Chung, D. W., J. S. Kim, and S. K. Kul. “Unified
voltage modulation technique for real-time three-phase power conversion.”
*IEEE Transactions on Industry Applications*. Vol. 34, no. 2,
1998, pp. 374–380.

[4] Hava, A. M., R. J. Kerkman, and T. A. Lipo. “Simple
analytical and graphical methods for carrier-based PWM-VSI drives.”
*IEEE Transactions on Power Electronics.* Vol. 14, 1999, no. 1,
pp. 49–61.

## Extended Capabilities

## Version History

**Introduced in R2015a**