# Bidirectional DC-DC Converter

Controller-driven bidirectional DC-DC step-up and step-down voltage regulator

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• Simscape / Electrical / Semiconductors & Converters / Converters

## Description

The Bidirectional DC-DC Converter block represents a converter that steps up or steps down DC voltage from either side of the converter to the other as driven by an attached controller and gate-signal generator. Bidirectional DC-DC converters are useful for switching between energy storage and use, for example, in electric vehicles.

The Bidirectional DC-DC Converter block allows you to model a nonisolated converter with two switching devices, an isolated converter with six switching devices, or a dual active bridge converter with eight switching devices. Options for the type of switching devices are:

• GTO — Gate turn-off thyristor. For information about the I-V characteristic of the device, see GTO.

• Ideal semiconductor switch — For information about the I-V characteristic of the device, see Ideal Semiconductor Switch.

• IGBT — Insulated-gate bipolar transistor. For information about the I-V characteristic of the device, see IGBT (Ideal, Switching).

• MOSFET — N-channel metal-oxide-semiconductor field-effect transistor. For information about the I-V characteristic of the device, see MOSFET (Ideal, Switching).

• Thyristor — For information about the I-V characteristic of the device, see Thyristor (Piecewise Linear).

• Averaged Switch — Semiconductor switch with an anti-parallel diode. The control signal port, G, accepts values in the `[0,1]` interval. When the value at port G is equal to `0` or `1`, the averaged switch is either fully opened or fully closed, and it behaves similarly to the Ideal Semiconductor Switch block with an anti-parallel diode. When the value at port G is between `0` and `1`, the averaged switch is partly opened. You can then average the PWM signal over a specified period. This allows for undersampling of the model or using modulation waveforms instead of PWM signals.

### Model

You can model three different types of bidirectional DC-DC converter. To access the different options, double-click the block and set the Modeling option parameter to either:

• `Nonisolated converter` — Bidirectional DC-DC converter without an electrical barrier. This converter contains an inductor, two capacitors, and two switches that are of the same device type.

• `Isolated converter` — Bidirectional DC-DC converter with an electrical barrier. This converter contains four additional switches that form a full bridge. The full bridge is on the input or high-voltage (HV) side of the converter. The other two switches are on the output or low-voltage (LV) side of the converter. You can select different semiconductor types for the HV and LV switching devices. For example, you can use a GTO for the HV switching devices and an IGBT for the LV switching devices. To provide separation between the input and output voltages, the model uses a high-frequency transformer.

• `Dual Active Bridge converter` — This bidirectional DC-DC converter contains two full-bridges. The left bridge is the input or high-voltage (HV) side of the converter. The right bridge is the output or low-voltage (LV) side of the converter. You can select different semiconductor types for the HV and LV switching devices. For example, you can use a GTO for the HV switching devices and an IGBT for the LV switching devices. To provide separation between the input and output voltages, the model uses a high-frequency transformer.

### Protection

The block contains an integral protection diode for each switching device. The integral diode protects the semiconductor device by providing a conduction path for reverse current. An inductive load can produce a high reverse-voltage spike when the semiconductor device suddenly switches off the voltage supply to the load.

To configure the internal protection diode block, use the Protection Diode parameters. This table shows how to set the Model dynamics parameter based on your goals.

GoalsValue to SelectIntegral Protection Diode
Prioritize simulation speed.`Diode with no dynamics`The Diode block
Prioritize model fidelity by precisely specifying reverse-mode charge dynamics.`Diode with charge dynamics`The dynamic model of the Diode block

You can also include a snubber circuit for each switching device. Snubber circuits contain a series-connected resistor and capacitor. They protect switching devices against high voltages that inductive loads produce when the device turns off the voltage supply to the load. Snubber circuits also prevent excessive rates of current change when a switching device turns on.

To include and configure a snubber circuit for each switching device, use the Snubbers parameters.

### Gate Control

To connect Simulink® gate-control voltage signals to the gate ports of the switching devices:

1. Convert each voltage signal using a Simulink-PS Converter block.

2. Multiplex the converted gate signals into a single vector.

3. Connect the vector signal to the G port.

### Piecewise Constant Approximation in Averaged Switch for FPGA Deployment

If you set the Switching device parameter to `Averaged switch` and your model uses a partitioning solver, this block produces nonlinear partitions because the average mode equations include modes, Gsat that are functions of the input G. To make these equations compatible with hardware description language (HDL) code generation, and therefore FPGA deployment, set the Integer for piecewise constant approximation of gate input (0 for disabled) parameter to a value greater than `0`. This block then treats the Gsat mode as a piecewise constant integer with a fixed range. This turns the previously nonlinear partitions to linear time varying partitions.

An integer value in the range `[0,K]`, where K is the value of the Integer for piecewise constant approximation of gate input (0 for disabled), is now associated with each real value mode in the range `[0,1]`. The block computes the piecewise constant mode by dividing the original mode by K to normalize it back to the range `[0,1]`:

`$\begin{array}{l}{u}_{I}=\left(floor\left(u\cdot K\right)\right)\\ \stackrel{^}{u}=\frac{{u}_{I}}{K}\end{array}$`

### Assumptions

A source impedance or a nonzero equivalent-series resistance (ESR) is connected to the left side of the Bidirectional DC-DC Converter block.

### 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.

## Ports

### Conserving

expand all

Electrical conserving port associated with the gate terminals of the switching devices.

Data Types: `double`

Electrical conserving port associated with the positive terminal of the first DC voltage.

Data Types: `double`

Electrical conserving port associated with the negative terminal of the first DC voltage.

Data Types: `double`

Electrical conserving port associated with the positive terminal of the second DC voltage.

Data Types: `double`

Electrical conserving port associated with the negative terminal of the second DC voltage.

Data Types: `double`

## Parameters

expand all

Whether to model a nonisolated converter with two switching devices, an isolated converter with six switching devices, or a dual active bridge converter with eight switching devices.

### Switching Devices

These tables show how the visibility of Switching Devices parameters depends on the converter model and switching devices that you select. To learn how to read the table, see Parameter Dependencies.

Nonisolated Converter Switching Devices Parameter Dependencies

Parameters and Options
Switching device
```Ideal Semiconductor Switch````GTO``IGBT``MOSFET``Thyristor````Averaged Switch```
On-state resistanceForward voltageForward voltageDrain-source on resistanceForward voltageOn-state resistance
Off-state conductanceOn-state resistanceOn-state resistanceOff-state conductanceOn-state resistance
Threshold voltageOff-state conductanceOff-state conductanceThreshold voltageOff-state conductance
Gate trigger voltage, VgtThreshold voltageGate trigger voltage, VgtInteger for piecewise constant approximation of gate input (0 for disabled)
Gate turn-off voltage, Vgt_offGate turn-off voltage, Vgt_off
Holding currentHolding current

Isolated Converter and Dual Active Bridge Converter Switching Devices Parameter Dependencies

Parameters and Options
Switching device HV
```Ideal Semiconductor Switch````GTO``IGBT``MOSFET``Thyristor````Averaged Switch```
On-state resistance HVForward voltage HVForward voltage HVDrain-source on resistance HVForward voltage HVOn-state resistance HV
Off-state conductance HVOn-state resistance HVOn-state resistance HVOff-state conductance HVOn-state resistance HV
Threshold voltage HVOff-state conductance HVOff-state conductance HVThreshold voltage HVOff-state conductance HV
Gate trigger voltage HV, Vgt_hvThreshold voltage HVGate trigger voltage HV, Vgt_hvInteger for piecewise constant approximation of gate input (0 for disabled)
Gate turn-off voltage HV, Vgt_off_hvGate turn-off voltage HV, Vgt_off_hv
Holding current HVHolding current HV
Switching device LV
```Ideal Semiconductor Switch````GTO``IGBT``MOSFET``Thyristor````Averaged Switch```
On-state resistance LVForward voltage LVForward voltage LVDrain-source on resistance LVForward voltage LVOn-state resistance LV
Off-state conductance LVOn-state resistance LVOn-state resistance LVOff-state conductance LVOn-state resistance LV
Threshold voltage LVOff-state conductance LVOff-state conductance LVThreshold voltage LVOff-state conductance LV
Gate trigger voltage LV, VgtThreshold voltage LVGate trigger voltage LV, VgtInteger for piecewise constant approximation of gate input (0 for disabled)
Gate turn-off voltage LV, Vgt_off_lvGate turn-off voltage LV, Vgt_off_lv
Holding current LVHolding current LV

Switching device type for the nonisolated converter model.

#### Dependencies

For the different switching device types, the Forward voltage is taken as:

• GTO — Minimum voltage required across the anode and cathode block ports for the gradient of the device I-V characteristic to be 1/Ron, where Ron is the value of On-state resistance

• IGBT — Minimum voltage required across the collector and emitter block ports for the gradient of the diode i-v characteristic to be 1/Ron, where Ron is the value of On-state resistance

• Thyristor — Minimum voltage required for the device to turn on

#### Dependencies

For the different switching device types, the On-state resistance is taken as:

• GTO — Rate of change of voltage versus current above the forward voltage

• Ideal semiconductor switch — Anode-cathode resistance when the device is on

• IGBT — Collector-emitter resistance when the device is on

• Thyristor — Anode-cathode resistance when the device is on

• Averaged switch — Anode-cathode resistance when the device is on

#### Dependencies

Resistance between the drain and the source, which also depends on the gate-to-source voltage.

#### Dependencies

Conductance when the device is off. The value must be less than 1/R, where R is the value of On-state resistance.

For the different switching device types, the On-state resistance is taken as:

• GTO — Anode-cathode conductance

• Ideal semiconductor switch — Anode-cathode conductance

• IGBT — Collector-emitter conductance

• MOSFET — Drain-source conductance

• Thyristor — Anode-cathode conductance

#### Dependencies

Gate voltage threshold. The device turns on when the gate voltage is above this value. For the different switching device types, the device voltage of interest is:

• Ideal semiconductor switch — Gate-emitter voltage

• IGBT — Gate-cathode voltage

• MOSFET — Gate-source voltage

#### Dependencies

Gate-cathode voltage threshold. The device turns on when the gate-cathode voltage is above this value.

#### Dependencies

Gate-cathode voltage threshold. The device turns off when the gate-cathode voltage is below this value.

#### Dependencies

Gate current threshold. The device stays on when the current is above this value, even when the gate-cathode voltage falls below the gate trigger voltage.

#### Dependencies

Switching device type for the high-voltage side of the isolated converter model.

#### Dependencies

For the different switching device types, the Forward voltage HV is taken as:

• GTO — Minimum voltage required across the anode and cathode block ports for the gradient of the device I-V characteristic to be 1/Ron, where Ron is the value of On-state resistance

• IGBT — Minimum voltage required across the collector and emitter block ports for the gradient of the diode i-v characteristic to be 1/Ron, where Ron is the value of On-state resistance

• Thyristor — Minimum voltage required for the device to turn on

#### Dependencies

Resistance between the drain and the source, which also depends on the gate-to-source voltage.

#### Dependencies

For the different switching device types, the On-state resistance HV is taken as:

• GTO — Rate of change of voltage versus current above the forward voltage

• Ideal semiconductor switch — Anode-cathode resistance when the device is on

• IGBT — Collector-emitter resistance when the device is on

• Thyristor — Anode-cathode resistance when the device is on

• Averaged switch — Anode-cathode resistance when the device is on

#### Dependencies

Conductance when the device is off. The value must be less than 1/R, where R is the value of On-state resistance HV.

For the different switching device types, the On-state resistance HV is taken as:

• GTO — Anode-cathode conductance

• Ideal semiconductor switch — Anode-cathode conductance

• IGBT — Collector-emitter conductance

• MOSFET — Drain-source conductance

• Thyristor — Anode-cathode conductance

#### Dependencies

Gate voltage threshold. The device turns on when the gate voltage is above this value. For the different switching device types, the device voltage of interest is:

• Ideal semiconductor switch — Gate-emitter voltage

• IGBT — Gate-cathode voltage

• MOSFET — Gate-source voltage

#### Dependencies

Gate-cathode voltage threshold. The device turns on when the gate-cathode voltage is above this value.

#### Dependencies

Gate-cathode voltage threshold. The device turns off when the gate-cathode voltage is below this value.

#### Dependencies

Gate current threshold. The device stays on when the current is above this value, even when the gate-cathode voltage falls below the gate trigger voltage.

#### Dependencies

Switching device type for the low-voltage side of the isolated converter model.

#### Dependencies

For the different switching device types, the Forward voltage LV is taken as:

• GTO — Minimum voltage required across the anode and cathode block ports for the gradient of the device I-V characteristic to be 1/Ron, where Ron is the value of On-state resistance

• IGBT — Minimum voltage required across the collector and emitter block ports for the gradient of the diode i-v characteristic to be 1/Ron, where Ron is the value of On-state resistance

• Thyristor — Minimum voltage required for the device to turn on

#### Dependencies

Resistance between the drain and the source, which also depends on the gate-to-source voltage.

#### Dependencies

For the different switching device types, the On-state resistance LV is taken as:

• GTO — Rate of change of voltage versus current above the forward voltage

• Ideal semiconductor switch — Anode-cathode resistance when the device is on

• IGBT — Collector-emitter resistance when the device is on

• Thyristor — Anode-cathode resistance when the device is on

• Averaged switch — Anode-cathode resistance when the device is on

#### Dependencies

Conductance when the device is off. The value must be less than 1/R, where R is the value of On-state resistance LV.

For the different switching device types, the On-state resistance LV is taken as:

• GTO — Anode-cathode conductance

• Ideal semiconductor switch — Anode-cathode conductance

• IGBT — Collector-emitter conductance

• MOSFET — Drain-source conductance

• Thyristor — Anode-cathode conductance

#### Dependencies

Gate voltage threshold. The device turns on when the gate voltage is above this value. For the different switching device types, the device voltage of interest is:

• Ideal semiconductor switch — Gate-emitter voltage

• IGBT — Gate-cathode voltage

• MOSFET — Gate-source voltage

#### Dependencies

Gate-cathode voltage threshold. The device turns on when the gate-cathode voltage is above this value.

#### Dependencies

Gate-cathode voltage threshold. The device turns off when the gate-cathode voltage is below this value.

#### Dependencies

Gate current threshold. The device stays on when the current is above this value, even when the gate-cathode voltage falls below the gate trigger voltage.

#### Dependencies

Integer used to perform piecewise constant approximation of the gate input for FPGA deployment.

#### Dependencies

To enable this parameter, set Switching device to `Averaged Switch`.

### Protection Diode

The visibility of Protection Diode parameters depends on how you configure the protection diode Model dynamics and Reverse recovery time parameterization parameters. To learn how to read this table, see Parameter Dependencies.

Protection Diode Parameter Dependencies

Parameters and Options
Model dynamics
Diode with no dynamicsDiode with charge dynamics
Forward voltageForward voltage
On resistanceOn resistance
Off conductanceOff conductance
Junction capacitance
Peak reverse current, iRM
Initial forward current when measuring iRM
Rate of change of current when measuring iRM
Reverse recovery time parameterization
```Specify stretch factor``````Specify reverse recovery time directly``````Specify reverse recovery charge```
Reverse recovery time stretch factorReverse recovery time, trrReverse recovery charge, Qrr

Diode type. The options are:

• `Diode with no dynamics` — Select this option to prioritize simulation speed using the Diode block.

• `Diode with charge dynamics` — Select this option to prioritize model fidelity in terms of reverse mode charge dynamics using the commutation diode model of the Diode block.

Note

If you select `Averaged Switch` for the Switching Device parameter in the Switching Device setting, this parameter is not visible and ```Diode with no dynamics``` is automatically selected.

#### Dependencies

See the Protection Diode Parameter Dependencies table.

Minimum voltage required across the positive and negative block ports for the gradient of the diode I-V characteristic to be 1/Ron, where Ron is the value of On resistance.

Rate of change of voltage versus current above the Forward voltage.

Conductance of the reverse-biased diode.

Diode junction capacitance.

#### Dependencies

See the Protection Diode Parameter Dependencies table.

Peak reverse current measured by an external test circuit.

#### Dependencies

See the Protection Diode Parameter Dependencies table.

Initial forward current when measuring peak reverse current. This value must be greater than zero.

#### Dependencies

See the Protection Diode Parameter Dependencies table.

Rate of change of current when measuring peak reverse current.

#### Dependencies

See the Protection Diode Parameter Dependencies table.

Model for parameterizing the recovery time. When you select `Specify stretch factor` or `Specify reverse recovery charge`, you can specify a value that the block uses to derive the reverse recovery time. For more information on these options, see How the Block Calculates TM and Tau.

#### Dependencies

See the Protection Diode Parameter Dependencies table.

Value that the block uses to calculate Reverse recovery time, trr. Specifying the stretch factor is an easier way to parameterize the reverse recovery time than specifying the reverse recovery charge. The larger the value of the stretch factor, the longer it takes for the reverse recovery current to dissipate.

#### Dependencies

See the Protection Diode Parameter Dependencies table.

Interval between the time when the current initially goes to zero (when the diode turns off) and the time when the current falls to less than 10 percent of the peak reverse current.

The value of the Reverse recovery time, trr parameter must be greater than the value of the Peak reverse current, iRM parameter divided by the value of the Rate of change of current when measuring iRM parameter.

#### Dependencies

See the Protection Diode Parameter Dependencies table.

Value that the block uses to calculate Reverse recovery time, trr. Use this parameter if the data sheet for your diode device specifies a value for the reverse recovery charge instead of a value for the reverse recovery time.

The reverse recovery charge is the total charge that continues to dissipate when the diode turns off. The value must be less than $-\frac{{i}^{2}{}_{RM}}{2a},$

where:

• iRM is the value specified for Peak reverse current, iRM.

• a is the value specified for Rate of change of current when measuring iRM.

#### Dependencies

See the Protection Diode Parameter Dependencies table.

### Transformer

To enable these parameters, set Modeling option to `Isolated converter`.

Self-inductance of the first winding of the transformer.

#### Dependencies

To enable this parameter, set Modeling option to `Isolated converter`.

Self-inductance of the second winding of the transformer.

#### Dependencies

To enable this parameter, set Modeling option to `Isolated converter`.

Defines the mutual inductance of the transformer.

#### Dependencies

To enable this parameter, set Modeling option to `Isolated converter`.

### LC Parameters

Converter inductance. If you set the Modeling option parameter to ```Isolated converter```, the two inductors are identical.

Series resistance of the inductor.

Capacitance of the first DC terminal.

Capacitance of the second DC terminal.

Series resistance of capacitor C1.

Series resistance of capacitor C2.

### Snubbers

The Snubbers parameters tab is not visible if you set Switching device to ```Averaged Switch```.

The table summarizes the Snubbers parameter dependencies. To learn how to read the table, see Parameter Dependencies.

Snubbers Parameter Dependencies

Snubbers Parameter Dependencies
Modeling option
```Nonisolated Converter``````Isolated Converter```
SnubberSnubber HV
`None````RC Snubber````None````RC Snubber```
Snubber resistanceSnubber resistance HV
Snubber capacitanceSnubber capacitance HV
Snubber LV
`None````RC Snubber```
Snubber resistance LV
Snubber capacitance LV

Snubber for each switching device.

#### Dependencies

See the Snubbers Parameter Dependencies table.

Resistance of the snubbers.

#### Dependencies

See the Snubbers Parameter Dependencies table.

Capacitance of the snubbers.

#### Dependencies

See the Snubbers Parameter Dependencies table.

HV snubber for each switching device.

#### Dependencies

See the Snubbers Parameter Dependencies table.

Resistance of the high-voltage snubbers.

#### Dependencies

See the Snubbers Parameter Dependencies table.

Capacitance of the high-voltage snubbers.

#### Dependencies

See the Snubbers Parameter Dependencies table.

LV snubber for each switching device.

#### Dependencies

See the Snubbers Parameter Dependencies table.

Resistance of the low-voltage snubbers.

#### Dependencies

See the Snubbers Parameter Dependencies table.

Capacitance of the low-voltage snubbers.

#### Dependencies

See the Snubbers Parameter Dependencies table.

## References

[1] Saleh, M., Y. Esa, Y. Mhandi, W. Brandauer, and A. Mohamed. Design and implementation of CCNY DC microgrid testbed. Industry Applications Society Annual Meeting. Portland, OR: 2016, pp 1-7.

[2] Kutkut, N. H., and G. Luckjiff. Current mode control of a full bridge DC-to-DC converter with a two inductor rectifier. Power Electronics Specialists Conference. Saint Louis, MO: 1997, pp 203-209.

[3] Nene, H. Digital control of a bi-directional DC-DC converter for automotive applications. Twenty-Eighth Annual IEEE Applied Power Electronics Conference and Exposition (APEC). Long Beach, CA: 2013, pp 1360-1365.

## Version History

Introduced in R2018a