Converter (Three-Phase, DQ0)

R2026b

Three-phase bidirectional AC/DC converter in direct-quadrature-zero reference frame

Since R2026b

• 

Converter (Three-Phase, DQ0) block

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Libraries:
Simscape / Electrical / DQ0 Components / Converters

Description

The Converter (Three-Phase, DQ0) block converts electrical power from AC to DC or from DC to AC. The block operates using either a three‑element Vdq0 voltage input or a two‑element Vdq input.

Equations

This equation defines the balance of power in the block:

$$i_{dc}{v}_{dc}=P_{AC}+P_{\text{loss}},$$

where:

• i_dc is the DC-link current flowing into the converter.

• v_dc is the DC-link voltage at the converter DC terminals.

• P_loss represents the total power loss in the converter.

• $$P_{AC}=\frac{3}{2}\left(v_d{i}_d+v_q{i}_q+2v_0{i}_0\right)$$ is the AC-side power.

• v_d is the d-axis voltage.

• i_d is the d-axis current.

• v_q is the q-axis voltage.

• i_q is the q-axis current.

• v₀ is the zero-sequence voltage.

• i₀ is the zero-sequence current.

Parameterize Losses

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

This equation defines the switching losses

$$P_{\text{switching}}=k_s{v}_{dc}{I}_{rms},$$

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.

• $$I_{rms}=\frac{\sqrt{i_d^2+i_q^2+2i_0^2}}{\sqrt{2}}$$ is the root mean squared (RMS) phase current.

This equation defines the conduction losses

$$P_{\text{conduction}}=k_{c1}{I}_{rms}+k_{c2}{I}_{rms}^2$$

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.

The Fixed power loss parameter defines the quiescent losses, P_fixed.

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

$$P_{\text{loss}}=P_{\text{switching}}+P_{\text{conduction}}+P_{\text{fixed}}.$$

If the k_s, k_c1, k_c2, and P_fixed parameters values are not available, then you can obtain them from the power losses profile instead, by setting the Losses parameterization parameter to Profile: loss=f(Irms,vdc_nom). To calculate the values of the parameters, the block solves the equation

$$\left[\begin{array}{c}{P}_1\\ ⋮\\ P_n\end{array}\right]=\left[\begin{array}{cccc}1& v_{dc\_nom}{I}_{rms,1}& I_{rms,1}& I_{rms,1}^2\\ ⋮& ⋮& ⋮& ⋮\\ 1& v_{dc\_nom}{I}_{rms,n}& I_{rms,n}& I_{rms,n}^2\end{array}\right]\left[\begin{array}{c}{P}_{fixed}\\ k_s\\ k_{c1}\\ k_{c2}\end{array}\right]$$

where:

• $$\left[\begin{array}{c}{P}_1\\ ⋮\\ P_n\end{array}\right]$$ is the vector of power loss values. Specify this vector by using the Converter losses parameter.

• v_{dc_nom} is equal to the Nominal dc-link voltage parameter value.

• $$\left[\begin{array}{c}{I}_{rms,1}\\ ⋮\\ I_{rms,}{}_n\end{array}\right]$$ is the vector of root mean square currents associated to the values of the Converter losses parameter. Specify this vector by using the RMS current for converter losses parameter.

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 prior to 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. Nominal values can come from different sources, one of which is the Nominal Values section in the block dialog box or Property Inspector. For more information, see System Scaling by Nominal Values.

To enable the Initial Targets and Nominal Values sections in this block, set the Modeling option parameter to Show thermal port.

Examples

Control Torque of IPMSM Inside Axle-Drive EV in DQ Frame

Models an interior permanent magnet synchronous machine (IPMSM) propelling a simplified axle-drive electric vehicle. The example controls and simulates the torque in the rotor direct-quadrature (DQ) reference frame. The IPMSM operates in both motoring and generating modes. A fixed-ratio gear-reduction model implements the vehicle transmission and differential. The Vehicle Controller subsystem converts the driver inputs into a relevant torque command. The Drive Controller subsystem controls the torque of the IPMSM. The control algorithm is implemented in continuous time. To simulate this model faster, this example uses a variable-step solver. The Scopes subsystem contains scopes that allow you to see the simulation results.

• Since R2025a
• Open Model

Control Torque of IPMSM Inside Parallel HEV in DQ Frame

Models a simplified parallel hybrid electric vehicle (HEV). An interior permanent magnet synchronous machine (IPMSM) and an internal combustion engine (ICE) provide the vehicle propulsion. This example controls and simulates the torque in the rotor direct-quadrature (DQ) reference frame. The IPMSM operates in both motoring and generating modes. A fixed-ratio gear-reduction model implements the vehicle transmission and differential. The Vehicle Controller subsystem converts the driver inputs into torque commands. A Stateflow® chart implements the vehicle control strategy. The ICE Controller subsystem controls the torque of the combustion engine. The EM Controller subsystem controls the torque of the IPMSM. To simulate this model faster, this example uses a variable-step solver. The Scopes subsystem contains scopes that allow you to see the simulation results.

• Since R2025a
• Open Model

Assumptions and Limitations

This block defines the dq0 quantities in the synchronous reference frame using the standard power-variant form. For more information about the Park transform, see Park Transform.

Ports

Inputs

Vdq0 — dq0 voltages, V

vector

Physical signal input port associated with the dq0 voltages.

Dependencies

To enable this port, set Zero sequence to Include.

Vdq — dq voltages, V

vector

Physical signal input port associated with the dq voltages.

Dependencies

To enable this port, set Zero sequence to Exclude.

Conserving

Note

The d, q, and 0 ports are electrical conserving ports that represent three‑phase quantities expressed in the rotating reference (dq0) frame. Connecting these ports to components outside the dq0 domain requires appropriate transformations to avoid modeling inconsistencies.

d — d-axis voltage

electrical

Electrical conserving port associated with the d-axis voltage.

q — q-axis voltage

electrical

Electrical conserving port associated with the q-axis voltage.

0 — Zero-sequence component

electrical

Electrical conserving port associated with the zero-sequence component.

Dependencies

To enable this port, set Zero sequence to Include.

+ — 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 of the converter.

Dependencies

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

Parameters

Modeling option — Option to enable thermal port

No thermal port (default) | Show thermal port

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

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. 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 block obtains the total power losses by summing 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 the block calculates it from the power losses profile.

Zero sequence — Option to include zero-sequence component

Include (default) | Exclude

Option to include or exclude the zero-sequence component.

Fixed power loss — Power loss

1 W (default) | positive scalar

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

Dependencies

To enable this parameter, set Losses parameterization to 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 converter power loss 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 RMS currents associated with 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] Rajput, M. N. Thermal Modeling of Permanent Magnet Synchronous Motor and Inverter. Master’s thesis, Georgia Institute of Technology, 2016.

Extended Capabilities

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

Version History

Introduced in R2026b