Build and Simulate a Single-Phase Half-Bridge Inverter with Ideal Switches

In this example, you build and analyze a single-phase, half-bridge inverter that you control by using sinusoidal pulse-width modulation (SPWM).

To see the completed version of the model you create in this example, at the MATLAB^® command prompt, enter SinglePhaseHalfBridgeInverterModel.

Build the Model

The single-phase, half-bridge inverter in this example consists of a power circuit and a control system. First, create both parts of the model by adding and connecting the blocks.

Build the Power Circuit

The power circuit comprises a DC link, two semiconductor switches with their anti-parallel diodes, and an inductive load.

To build the power circuit:

Create a new model.

Add the blocks in this table. The Library Path column specifies the hierarchical path to each block.

Block	Purpose	Library Path	Quantity
DC Voltage Source	Provide a DC link	Simscape > Foundation Library > Electrical > Electrical Sources	2
IGBT (Ideal, Switching)	Model two semiconductor switches with their anti-parallel diodes and build the half-bridge	Simscape > Electrical > Semiconductor & Converters	2
Inductor	Model an inductive load	Simscape > Foundation Library > Electrical > Electrical Elements	1
Electrical Reference	Provide the ground connection for the electrical conserving ports	Simscape > Foundation Library > Electrical > Electrical Elements	1
Voltage Sensor	Measure the voltage across the load	Simscape > Foundation Library > Electrical > Electrical Sensors	1
Current Sensor	Measure the current that flows through the load	Simscape > Foundation Library > Electrical > Electrical Sensors	1
Solver Configuration	Define the solver settings that apply to all physical modeling blocks	Simscape > Utilities	1
Simulink-PS Converter	Convert an output physical signal to a Simulink signal	Simscape > Utilities	2
PS-Simulink Converter	Convert a Simulink input signal into a physical signal	Simscape > Utilities	2
Scope	Display the load voltage and the current wave	Simulink > Commonly Used Blocks	2

Note

You can use the Simscape™ function sscnew with a domain type of electrical to create a Simscape model that contains these blocks:

Simulink-PS Converter
PS-Simulink Converter
Scope
Solver Configuration
Electrical Reference

Rename and connect the blocks as shown in the diagram.

Build the Control System

The control system generates two pulse-width modulated (PWM) gate signals that control the switching behavior of the two IGBT blocks. If the gate signal value is equal to 1, the IGBT (Ideal, Switching) block turns on. If the gate signal value is equal to 0, the block turns off.

To build the control system:

Add the blocks in this table to the model. The Library Path column specifies the hierarchical path to each block.

Block	Purpose	Library Path	Quantity
Sine Wave	Generate a sinusoidal signal that represents a unit sinusoidal modulation wave	Simulink > Sources	1
Constant	Define the sinusoidal pulse-width modulation index	Simulink > Sources	1
Product	Obtain the sinusoidal modulation wave by multiplying the unit sinusoidal wave by the modulation index	Simulink > Math Operations	1
Bias	Perform calculation to obtain the duty cycle signal	Simulink > Math Operations	1
Gain	Perform calculation to obtain the duty cycle signal	Simulink > Math Operations	1
PWM Generator	Generate the PWM gate signal for the `IGBT1` block	Simscape > Electrical > Control > Pulse Width Modulation	1
Logical Operator	Obtain the complementary PWM gate signal for the `IGBT2` block	Simulink > Logic and Bit Operations	1
Data Type Conversion	Convert the input Boolean signal to double signal	Simulink > Signal Attributes	1
Goto	Pass the input PWM gate signal to the corresponding From block	Simulink > Signal Routing	2
From	Receive a PWM gate signal from the corresponding Goto block and pass the signal as an output	Simulink > Signal Routing	2

Rename and connect the blocks as shown in the diagram.

Specify Model Parameters

Specify these parameters to represent the behavior of the system components:

Model Setup Parameters
Power Circuit Parameters
Control System Parameters
Signal Display Parameters

Model Setup Parameters

These blocks specify model information that is not specific to a particular block:

Solver Configuration
Electrical Reference

As with Simscape models, you must include a Solver Configuration block in each topologically distinct physical network. This example has a single physical network, so use one Solver Configuration block with the default parameter values.

You must include an Electrical Reference block in each Simscape Electrical™ network. This block does not have any parameters.

Power Circuit Parameters

Specify these parameters to represent the behavior of the power circuit components:

Set the Constant voltage parameter of the two DC Voltage Source blocks to 100.
Set the parameters of the two IGBT (Ideal, Switching) blocks:
- Main settings
  - Forward voltage, Vf — 0.8
  - On-state resistance — 0.001
  - Off-state conductance — 1e-5
  - Threshold voltage, Vth — 0.5. With this value, the IGBT switches on when the value at the input port is equal to 1 and it switches off when the value at the input port is equal to 0.
- Integral Diode settings
  - Integral protection diode — Protection diode with no dynamics
  - Forward voltage — 0.8
  - On resistance — 0.001
  - Off conductance — 1e-5
Set the parameters of the Inductor block:
- Inductance — 0.005
- Series resistance — 1
- Parallel conductance — 0

Control System Parameters

Specify the following parameters to get the PWM gate signals for the IGBT1 and IGBT2 from a sinusoidal modulation wave:

In the Constant block, set the Constant value parameter to 0.8.
To generate a unit sinusoidal modulation wave, set the parameters of the Sine Wave block:
- Amplitude — 1
- Bias — 0
- Frequency (rad/sec) — 2*pi*60
- Phase (rad) — 0
- Sample time — 0
In the Bias block, set the Bias parameter to 1.
In the Gain block, set the Gain parameter to 0.5.
Set the PWM Generator block parameters:
- Carrier counter — Up-Down
- Timer period (s) — 1/2/2000
- Phase delay (s) — 0
- Sample time — 0
In the Logical Operator block, set the Operator parameter to NOT.

The sinusoidal modulation wave is equal to $0.8 \cdot \sin (2 π \cdot 60 \cdot t) .$ To change the modulation wave, modify the modulation index, frequency, and phase values.

The PWM Generator block cannot receive the modulation wave as an input, because it must be a duty cycle. To obtain the duty cycle from the modulation wave, this example uses this equation:

$D = \frac{M + 1}{2}$

where D is the duty cycle and M is the modulation wave. The Bias and Gain blocks of the control system implement this calculation.

The output PWM gate signal from the PWM Generator block controls the IGBT1 block. The Logical Operator block implements the complementary PWM gate signal that controls the IGBT2 block. The value of the Timer period (s) parameter of the PWM Generator block is equal to 1/2/2000, which means that the switching frequency is equal to 2 kHz.

The Goto blocks and From blocks implement the connection between the generated PWM gate signals and the two IGBT (Ideal, Switching) blocks. Setting the Goto tag parameter in a Goto and From block to the same tag allows you to pass a signal from one block to another without connecting them.

Signal Display Parameters

Specify the parameters of the Scope block to display the output signals.

Double-click the Scope blocks and then click the View > Configuration Properties to open the Scope Configuration Properties dialog box. On the Logging tab, clear the Limit data points to last check box.

Configure the Solver Parameters

Configure the solver parameters to use a continuous-time solver. Simscape Electrical models only run with a continuous-time solver when you clear the Local Solver parameter of a Solver Configuration block. Use the Configuration Parameters dialog box to change the simulation end time, tighten the relative tolerance for a more accurate simulation, and remove the limit on the number of simulation data points Simulink^® saves.

In the model window, select Modeling > Model Settings to open the Configuration Parameters dialog box.
In the left pane, click Solver:
- Set Stop time to 4/60.
- Set Solver to ode23t (Mod. stiff/Trapezoidal).
- Set Max step size to 1e-4.
- Set Relative tolerance to 1e-4.
Click OK.

For more information about configuring solver parameters, see Simulating an Electronic, Mechatronic, or Electrical Power System.

Simulate the Model and Analyze the Results

Run the simulation and plot the results. In the model window, select Simulation > Run.

To view the load voltage and current, double-click the Scope blocks. You can do this before or after you run the simulation.

This figure shows the load current.

The next figure shows the load voltage.

As expected, the load voltage is a PWM wave varying between -100 V and 100 V.

To view other simulation results, such as the current flowing through each IGBT (Ideal, Switching) block and its anti-parallel diode, use the Simscape Results Explorer. To enable the Simscape Results Explorer, first log the simulation data for all variables:

In the model window, select Modeling > Model Settings to open the Configuration Parameters dialog box.
In the left pane, click Simscape:
- Set Log simulation data to All.
- Select the Open viewer after simulation check box.
- Clear the Limit data points check box.
Click OK.

In the model window, select Simulation > Run to run the simulation. This figure shows the Simscape Results Explorer window that opens automatically.

When you click a node in the left pane, the corresponding plots appear in the right pane. For example, if you click the variable i in IGBT1 > ideal_switch, then the Simscape Results Explorer plots the current that flows through the IGBT1 block in the half-bridge.

To select several variables for side-by-side plot comparison, press Ctrl and click multiple variables. For example, check the current that flows through the IGBT1 block and the current that flows through the anti-parallel diode of the block:

For more information, see Simscape Results Explorer.