# Average-Value Voltage Source Converter (Three-Phase)

Average-value bidirectional AC/DC voltage source converter

Libraries:
Simscape / Electrical / Semiconductors & Converters / Converters

## Description

The Average-Value Voltage Source Converter (Three-Phase) block converts electrical energy from AC to DC voltage or from DC to AC voltage according to an input three-phase modulation wave. The corresponding input power is equal to the sum of the fixed power loss and the output power.

This block can work in both time and frequency-and-time simulation modes. If you set the AC frequency parameter to `Variable`, this block works only in time simulation mode. If you select `Constant`, this block works in both time and frequency-time simulation modes. For more information, see Frequency and Time Simulation Mode.

### Losses Parameterization

Switching losses, conduction losses, and quiescent losses are the main heat sources for a converter.

The switching losses are defined by this equation:

`${P}_{switching}={k}_{s}{v}_{dc}{I}_{rms}$`

where:

• ks is the proportionality constant that depends on the turn-on and turn-off intervals and switching frequency. Specify this value by setting the Switching losses coefficient, ks parameter.

• vdc is the dc-link voltage.

• ${I}_{rms}=\frac{\sqrt{{\left({i}_{a}-{i}_{dc}\right)}^{2}+{\left({i}_{b}-{i}_{dc}\right)}^{2}+{\left({i}_{c}-{i}_{dc}\right)}^{2}}}{\sqrt{3}}$ is the root mean square (RMS) phase current, where ${i}_{dc}=\frac{{i}_{a}+{i}_{b}+{i}_{c}}{3}.$

The conduction losses are defined by this equation:

`${P}_{conduction}={k}_{c1}{I}_{rms}+{k}_{c2}{I}_{rms}^{2}$`

where:

• kc1 is the coefficient of the conduction losses that depends on the on-state zero current collector-emitter voltage of the transistor and on the forward voltage drop of the diode. Specify this value by setting the Conduction losses coefficient, kc1 parameter.

• kc2 is the coefficient of the conduction losses that depends on the state resistance of the transistor and on the anti-parallel diode. Specify this value by setting the Conduction losses coefficient, kc2 parameter.

The quiescent losses are defined by the Fixed power loss parameter, Pfixed.

The sum of the switching, conduction, and quiescent losses define the total power losses of the converter:

`${P}_{loss}={P}_{switching}+{P}_{conduction}+{P}_{fixed}.$`

If not available, you can also obtain the ks, kc1, kc2 and Pfixed parameters values from the power losses profile, by setting the Losses parameterization parameter to `Profile: loss=f(Irms,vdc_nom)`. The block then solves this equation and calculates the values of the parameters:

`$\left[\begin{array}{c}{P}_{1}\\ ⋮\\ {P}_{n}\end{array}\right]=\left[\begin{array}{cccc}1& {v}_{dc_nom}{I}_{rms,1}& {I}_{rms,1}& {I}_{rms,1}^{2}\\ ⋮& ⋮& ⋮& ⋮\\ 1& {v}_{dc_nom}{I}_{rms,n}& {I}_{rms,n}& {I}_{rms,n}^{2}\end{array}\right]\left[\begin{array}{c}{P}_{fixed}\\ {k}_{s}\\ {k}_{c1}\\ {k}_{c2}\end{array}\right]$`

where $\left[\begin{array}{c}{P}_{1}\\ ⋮\\ {P}_{n}\end{array}\right]$ is the vector of power loss values, Converter losses, corresponding to the RMS current for converter losses parameter, $\left[\begin{array}{c}{I}_{rms,1}\\ ⋮\\ {I}_{rms,}{}_{n}\end{array}\right]$, and the Nominal dc-link voltage, vdc_nom.

### Model Thermal Effects

This block has one optional thermal port. To expose the thermal port, set the Modeling option parameter to either:

• `No thermal port` — The block does not contain a thermal port.

• `Show thermal port` — The block contains one thermal conserving port.

## Ports

### Input

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Physical signal input port associated with the normalized modulation wave.

### Conserving

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Expandable electrical conserving port associated with voltage. For more information, see three-phase port.

#### Dependencies

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

Electrical conserving port associated with a-phase.

#### Dependencies

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

Electrical conserving port associated with b-phase.

#### Dependencies

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

Electrical conserving port associated with c-phase.

#### Dependencies

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

Electrical conserving port associated with the positive terminal.

Electrical conserving port associated with the negative terminal.

Thermal conserving port.

#### Dependencies

To enable this port, set Modeling option to `Show thermal port`.

## Parameters

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Whether to enable the thermal port of the block and model thermal parameters.

Whether to have composite or expanded three-phase ports.

Whether to have a variable or constant AC frequency:

• `Variable` — If the frequency of generated AC voltage varies, this option supports both variable-voltage variable-frequency (VVVF) and variable-voltage constant-frequency (VVCF) applications but the block only works in time simulation mode.

• `Constant` — If the frequency of generated AC voltage is constant, this option supports variable-voltage constant-frequency (VVCF) application and the block works in both time and frequency-and-time simulation modes.

Rated electrical frequency. The value of this parameter must be equal to the value of the rated electrical frequencies of other sinusoidal sources in your model, if present.

#### Dependencies

To enable this parameter, set AC frequency to `Constant`.

Parameterization option for the power losses. You can choose one of these options:

• `Fixed` — Power loss is fixed and equal to the value of the Fixed power loss parameter.

• ```Coefficients: loss=Pfixed+ks*vdc*Irms+kc1*Irms+kc2*Irms^2``` — The total power losses are obtained by summing up the switching, the conduction, and quiescent losses.

• `Profile: loss=f(Irms,vdc_nom)` — The power loss is a function of the RMS current and the nominal dc-link voltage, and is obtained from the power losses profile.

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Fixed power loss on semiconductor components, in W. The input power is equal to the fixed power loss plus output power.

#### Dependencies

To enable this parameter, set Losses parameterization to either `Fixed` or ```Coefficients: loss=Pfixed+ks*vdc*Irms+kc1*Irms+kc2*Irms^2```.

Proportionality constant that depends on the turn-on and turn-off intervals and switching frequency.

#### Dependencies

To enable this parameter, set Losses parameterization to ```Coefficients: loss=Pfixed+ks*vdc*Irms+kc1*Irms+kc2*Irms^2```.

Coefficient of the conduction losses that depends on the on-state zero current collector-emitter voltage of the transistor and on the forward voltage drop of the diode.

#### Dependencies

To enable this parameter, set Losses parameterization to ```Coefficients: loss=Pfixed+ks*vdc*Irms+kc1*Irms+kc2*Irms^2```.

Coefficient of the conduction losses that depends on the state resistance of the transistor and on the anti-parallel diode.

#### Dependencies

To enable this parameter, set Losses parameterization to ```Coefficients: loss=Pfixed+ks*vdc*Irms+kc1*Irms+kc2*Irms^2```.

Vector of power losses values.

#### Dependencies

To enable this parameter, set Losses parameterization to ```Profile: loss=f(Irms,vdc_nom)```.

Vector of root mean square currents associated to the values of the Converter losses parameter.

#### Dependencies

To enable this parameter, set Losses parameterization to ```Profile: loss=f(Irms,vdc_nom)```.

Nominal voltage.

#### Dependencies

To enable this parameter, set Losses parameterization to ```Profile: loss=f(Irms,vdc_nom)```.

Thermal mass.

#### Dependencies

To enable this parameter, set Modeling option to `Show thermal port`.

## References

[1] Rajput, M. N. Thermal modeling of permanent magnet synchronous motor and inverter. 2016.

## Version History

Introduced in R2018a

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