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

Average-value bidirectional AC/DC voltage source converter

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• 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.

### 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.

### Thermal Port

The block has one optional thermal port. This port is hidden by default. To expose the thermal port, right-click the block in your model, select Simscape > Block choices, and then select the desired block variant with thermal ports: Composite three-phase ports | Show thermal port or Expanded three-phase ports | Show thermal port. This action displays the thermal port on the block icon, and enables the Thermal mass parameter.

## 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.

Electrical conserving port associated with the positive terminal.

Electrical conserving port associated with the negative terminal.

Thermal conserving port. To expose the thermal port, right-click the block in your model, select Simscape > Block choices, and then select the desired block variant with thermal ports. For more information, see Thermal Port.

## Parameters

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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, right-click the block in your model, select Simscape > Block choices, and then select the desired block variant with thermal ports.

## References

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