Average-Value Voltage Source Converter (Three-Phase)

Three-phase average-value bidirectional AC/DC voltage source converter

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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. You can specify the modulation wave directly or through phasor quantities such as the magnitude and phase shift. 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.

Enable or Disable Converter

Since R2026a

You can enable or disable the functionality of the Average-Value Voltage Source Converter (Three-Phase) block by selecting the Expose port to enable or disable converter parameter and applying a signal to the physical signal port ENA.

For a grid-connected voltage source converter, if you disable the converter by applying a signal of value 0 to the ENA port, the Average-Value Voltage Source Converter (Three-Phase) block operates as an average-value diode-based rectifier. If you enable the converter by applying a signal of value 1 to the ENA port, the block operates as a normal converter.

This figure shows the operation switching between the diode-based rectification and normal converter operation depending on the value at the ENA port.

For a grid-connected application, if you disable the converter, the modeling equations are:

$$\begin{array}{l}{V}_{\text{rms}}=\sqrt{\frac{{\left(v_a-v_b\right)}^2+{\left(v_b-v_c\right)}^2+{\left(v_c-v_a\right)}^2}{3}}\\ V_{\text{dc}}=3\frac{\sqrt{2}}{\pi }{V}_{\text{rms}}\\ P_{\text{dc}}=-V_{\text{dc}}{I}_{\text{dc}}\\ P_{\text{ac}}=P_{\text{dc}}+P_{\text{conduction}}\\ P_{\text{conduction}}=k_{\text{rec}}{I}_{\text{rms}}^2\\ I_{\text{rms}}=\sqrt{\frac{{\left(i_a-i_0\right)}^2+{\left(i_b-i_0\right)}^2+{\left(i_c-i_0\right)}^2}{3}}\\ i_0=\frac{i_a+i_b+i_c}{3}\\ R_{\text{ac}}=\frac{V_{\text{rms}}^2}{P_{\text{ac}}}\\ i_a=\frac{v_a}{R_{\text{ac}}}\\ i_b=\frac{v_b}{R_{\text{ac}}}\\ i_c=\frac{v_c}{R_{\text{ac}}}\end{array}$$

where:

• v_a, v_b, and v_c are the respective AC phase voltages.

• i_a, i_b, and i_c are the respective AC phase currents that flow in the converter.

• V_rms is the RMS AC line-line voltage.

• V_dc is the DC-side voltage.

• I_dc is the DC-side current that flows in the converter.

• P_dc is the DC-side power output.

• P_ac is the power that flows in the AC side of the converter.

• I_rms is the RMS phase current.

• i₀ is the zero-sequency current at the AC side of the converter.

• R_ac is the equivalent per-phase series resistance at the AC side of the converter.

If you enable the converter, the modeling equations are:

$$\begin{array}{l}{v}_a=\text{ModWave}\left(1\right)\cdot \frac{V_{\text{dc}}}{2}\\ v_b=\text{ModWave}\left(2\right)\cdot \frac{V_{\text{dc}}}{2}\\ v_c=\text{ModWave}\left(3\right)\cdot \frac{V_{\text{dc}}}{2}\\ P_{\text{ac}}=-\left(v_a{i}_a+v_b{i}_b+v_c{i}_c\right)\\ P_{\text{dc}}=P_{\text{ac}}+P_{\text{loss}}\\ I_{\text{dc}}=\frac{P_{\text{dc}}}{V_{\text{dc}}}\end{array}$$

where:

• v_a, v_b, and v_c are the respective AC phase voltages.

• i_a, i_b, and i_c are the respective AC phase currents that flow in the converter.

• V_dc is the DC-side voltage.

• I_dc is the DC-side current that flows in the converter.

• P_dc is the DC-side power output.

• P_ac is the power that flows in the AC side of the converter.

• P_loss is the total power loss of the converter.

• ModWave(1), ModWave(2), and ModWave(3) are the first, second, and third element of the vector at the ModWave input port, respectively.

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:

• k_s 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.

• v_dc 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:

• k_c1 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.

• k_c2 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.

If you disable the converter, the converter works as an average-value diode-based rectifier. In this scenario, the switching losses are negligible and the conduction losses are defined by this equation:

$$P_{conduction}=k_{rec}{I}_{rms}^2$$

where k_rec is the value of the Rectifier conduction losses coefficient, krec parameter. (since R2026a)

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

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 k_s, k_c1, k_c2 and P_fixed 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, v_{dc_nom}.

Model Thermal Effects

This block has one optional thermal port. To control the visibility of 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.

Variables

To set the priority and initial target values for the block variables before simulation, use the Initial Targets section in the block dialog box or Property Inspector. For more information, see Set Priority and Initial Target for Block Variables.

Nominal values provide a way to specify the expected magnitude of a variable in a model. Using system scaling based on nominal values increases the simulation robustness. You can specify nominal values using different sources, including the Nominal Values section in the block dialog box or Property Inspector. For more information, see System Scaling by Nominal Values.

Examples

Asynchronous Machine Direct Torque Control with Space Vector Modulator

Control an asynchronous machine (ASM) using the direct-torque control method with space vector modulator. A PI-based speed controller supplies the torque reference. The direct-torque controller generates the reference voltages required by the space vector modulator. A DC voltage source feeds the ASM through a controlled average-value voltage source converter.

• Open Model

Microgrid with Electric Vehicles V2G (Vehicle-to-Grid) Support

Model a microgrid and how to regulate its frequency by using vehicle-to-grid (V2G) support from electric vehicles (EVs).

• Open Model

Control Three-Phase Solar Inverter

Control a three-phase single-stage solar photovoltaic (PV) inverter using a Solar PV Controller (Three-Phase) block. In a grid-connected PV plant, a PV controller extracts the maximum power from the solar array and feeds it to the grid. To extract the maximum available PV power, the controller uses a maximum power point tracking (MPPT) algorithm.

• Since R2025a
• Open Live Script

Model Static Synchronous Compensator Using Voltage Source Converter

Models a hybrid var compensator that includes a static synchronous compensator (STATCOM) and a thyristor-switched capacitor (TSC).

• Since R2024a
• Open Model

Ports

Input

ModWave — Modulation wave

vector

Physical signal input port associated with the normalized modulation wave.

Dependencies

To enable this port, set Input type to Modulation wave.

Vt — Phase-to-phase RMS voltage

scalar

Since R2024a

Physical signal input port associated with the phase-to-phase RMS voltage.

Dependencies

To enable this port, set Input type to Sinusoidal magnitude and phase shift.

ph — Phase shift

scalar

Since R2024a

Physical signal input port associated with the phase shift.

Dependencies

To enable this port, set Input type to Sinusoidal magnitude and phase shift.

ENA — Enable or disable converter

scalar

Since R2026a

Physical signal input port associated with the converter functionality. To enable the converter, apply a signal value of 1 to this port. To disable the converter, apply a signal value of 0 to this port.

Dependencies

To enable this port, select the Expose port to enable or disable converter parameter.

Conserving

~ — Voltage

electrical

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.

a — a-phase

electrical

Electrical conserving port associated with a-phase.

Dependencies

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

b — b-phase

electrical

Electrical conserving port associated with b-phase.

Dependencies

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

c — c-phase

electrical

Electrical conserving port associated with c-phase.

Dependencies

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

+ — Positive terminal

electrical

Electrical conserving port associated with the positive terminal.

- — Negative terminal

electrical

Electrical conserving port associated with the negative terminal.

H — Thermal port

thermal

Thermal conserving port.

Dependencies

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

Parameters

Modeling option — Whether to enable thermal port

No thermal port (default) | Show thermal port

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

Electrical connection — Electrical connection

Composite three-phase ports (default) | Expanded three-phase ports

Whether to have composite or expanded three-phase ports.

Expose port to enable or disable converter — Option to expose port that enables or disables converter

Off (default) | On

Since R2026a

Option to expose a physical signal input port, ENA, that allows you to enable or disable the converter.

Rectifier conduction losses coefficient, krec — Coefficient of conduction losses

0.01 Ohm (default) | nonnegative scalar

Since R2026a

Coefficient of the conduction losses that depends on the on-state resistance of the anti-parallel diodes.

AC frequency — AC frequency

Variable (default) | Constant

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. You can also choose between a three-phase modulation wave input or a magnitude and phase modulation input.

Input type — Type of input

Modulation wave (default) | Sinusoidal magnitude and phase shift

Since R2024a

Option to specify the input of the block as a three-phase modulation wave or through sinusoidal magnitude and phase shift.

Dependencies

To enable this parameter, set AC frequency to Constant.

Rated electrical frequency — Rated electrical frequency

60 Hz | positive scalar

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.

Losses parameterization — Losses parameterization

Fixed (default) | Coefficients: loss=Pfixed+ks*vdc*Irms+kc1*Irms+kc2*Irms^2 | Profile: loss=f(Irms,vdc_nom)

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.

,

Fixed power loss — Power loss

1 W (default) | positive scalar

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.

Switching losses coefficient, ks — Coefficient of switching losses

0.01 (default) | nonnegative scalar

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.

Conduction losses coefficient, kc1 — First coefficient of conduction losses

1.7 V (default) | nonnegative scalar

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.

Conduction losses coefficient, kc2 — Second coefficient of conduction losses

0.01 Ohm (default) | nonnegative scalar

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.

Converter losses — Converter losses vector

[100, 800, 1870, 3250, 4900] W (default) | vector of positive elements

Vector of power losses values.

Dependencies

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

RMS current for converter losses — RMS currents vector

[10, 100, 200, 300, 400] A (default) | vector of positive elements

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 dc-link voltage — Nominal dc-link voltage

300 V (default) | positive scalar

Nominal voltage.

Dependencies

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

Thermal mass — Thermal mass

30000 J/K (default) | positive scalar

Thermal mass.

Dependencies

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

References

[1] M. N., Rajput. "Thermal modeling of permanent magnet synchronous motor and inverter." Master's Thesis, Georgia Institute of Technology, 2016. https://hdl.handle.net/1853/55053.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2018a

R2026a: Enable or disable converter

You can now enable or disable the functionality of the block by selecting the Expose port to enable or disable converter parameter and applying a signal to the physical signal port ENA.

If you disable the converter by applying a signal of value 0 to the ENA port, the Average-Value Voltage Source Converter (Three-Phase) block operates as an average-value diode-based rectifier. If you enable the converter by applying a signal of value 1 to the ENA port, the block operates as a normal converter.

R2024a: Specify magnitude and phase modulation input

You can now use phasor quantities such as magnitude and phase shift as input to the block. To specify a magnitude and phase modulation input, set the AC frequency parameter to Constant and the Input type parameter to Sinusoidal magnitude and phase shift.

R2021b: Electrical connection ports update

From R2021b forward, to switch between composite and expanded ports, set the Electrical connection parameter to either Composite three-phase ports or Expanded three-phase ports.

As a result of these changes, inside a model saved in an earlier release, review the Electrical connection parameter of this block.