Three-Phase Voltage Source Inverter

Three-phase voltage source inverter

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Libraries:
Powertrain Blockset / Propulsion / Electric Motors and Inverters

Description

The Three-Phase Voltage Source Inverter block implements a three-phase voltage source inverter that generates neutral voltage commands for a balanced three-phase load. Configure the voltage switching function for continuous vector modulation or inverter switch input signals. You can incorporate the block into a closed-loop model to simulate a power inverter. The block controls the ideal switch states.

To enable power loss calculations suitable for code generation targets that limit memory, select Enable memory optimized 2D LUT. Click Calibrate Maps to virtually calibrate an inverter power loss lookup table as a function of motor torque and motor speed.

If you select Input inverter temperature, click Calibrate Maps to virtually calibrate the power loss table as a function of motor torque, motor speed, and inverter temperature. You cannot enable memory optimization for the 3D power loss lookup table.

Use the Switching voltage function parameter to set the switching voltage function.

Setting	Implementation	Illustration
Commanded phase voltage	Phase a, b, c line-to-neutral voltage command input. Suitable for continuous sinusoidal or space vector modulation input signals.
Switch inputs (default)	Inverter switch input command. Suitable for hardware-in-the-loop (HIL) simulation. The inverter switches S1, S3, and S5 using complemented control for S2, S4, and S6.

Virtual Calibration

If you have Model-Based Calibration Toolbox™, click Calibrate Maps to virtually calibrate the lookup tables using measured data. The dialog box steps through these tasks.

Task	Description
Import Loss Data	Import this loss data from a file. For example, open <matlabroot>/toolbox/autoblks/autoblksshared/mbctemplates/MappedInverterDataset.xlsx. For more information, see Using Data (Model-Based Calibration Toolbox). Input inverter temperature Setting Required Data off Motor speed, rad/s Motor torque, N·m Power loss, W on Motor speed, rad/s Motor torque, N·m Motor temperature, K Power loss, W Collect inverter data at steady-state operating conditions. Data should cover the inverter speed, torque, and temperature operating range. To filter or edit the data, select Edit in Application. The Model-Based Calibration Toolbox Data Editor opens.
Generate Response Models	Model-Based Calibration Toolbox uses test plans to fit data to Gaussian process models (GPMs). To assess or adjust the response model fit, select Edit in Application. The Model-Based Calibration Toolbox Model Browser opens. For more information, see Model Assessment (Model-Based Calibration Toolbox).
Generate Calibration	Model-Based Calibration Toolbox calibrates the response models and generates calibrated tables. To assess or adjust the calibration, select Edit in Application. The Model-Based Calibration Toolbox CAGE Browser opens. For more information, see Calibration Lookup Tables (Model-Based Calibration Toolbox).
Update block parameters	Update these parameters with the calibration. Input inverter temperature Setting Parameters off Vector of speeds (w) for tabulated losses, w_eff_bp Vector of torques (T) for tabulated losses, T_eff_bp Corresponding power loss, ploss_table on Vector of speeds (w) for tabulated losses, w_eff_bp Vector of torques (T) for tabulated losses, T_eff_bp Vector of temperatures for tabulated losses, Temp_eff_bp Corresponding power loss, ploss_table_3d

Switching Function

For the switch voltage, the block implementation depends on the Switching voltage function setting.

Setting	Calculation	Equations
Commanded phase voltage	Continuous line-to-neutral voltage commands set to phase a, b, c line-to-neutral voltage command input	$$\begin{array}{l}{v}_{an}=v_{a\_cmd}\\ v_{bn}=v_{b\_cmd}\\ v_{cn}=v_{c\_cmd}\end{array}$$
	Line-to-line voltage	$\begin{array}{l}{v}_{ab}= v_{an}- v_{bn}\\ v_{bc}= v_{bn}- v_{cn}\\ v_{ca}= v_{cn}- v_{an}\end{array}$
Switch inputs	Switching function	$$\begin{array}{l}S{F}_a=\{\begin{array}{c}1\text{ S}1\text{ on and S2 off}\\ -1\text{ S}1\text{ off and S2 on}\end{array}\\ \\ S{F}_b=\{\begin{array}{c}1\text{ S}3\text{ on and S4 off}\\ -1\text{ S}3\text{ off and S4 on}\end{array}\\ \\ S{F}_c=\{\begin{array}{c}1\text{ S}5\text{ on and S6 off}\\ -1\text{ S}5\text{ off and S6 on}\end{array}\end{array}$$
	Line-to-center point voltage	$$\begin{array}{l}{v}_{ao}= \frac{v_{bus}}{2} S{F}_a\\ v_{bo}= \frac{v_{bus}}{2} S{F}_b\\ v_{co}= \frac{v_{bus}}{2} S{F}_c\end{array}$$
	Line-to-neutral voltage	$\begin{array}{l}{v}_{an}= v_{ao}- v_{no}\\ v_{bn}= v_{bo}- v_{no}\\ v_{cn}= v_{co}- v_{no}\\ \\ v_{an}+ v_{bn}+ v_{cn}= 0\\ \\ v_{no}= \frac{1}{3}\left(v_{ao}+ v_{bo}+ v_{co}\right)\\ \\ v_{an}= v_{ao}- \frac{1}{3}\left(v_{ao}+ v_{bo}+ v_{co}\right)\\ v_{bn}= v_{bo}-\frac{1}{3}\left(v_{ao}+ v_{bo}+ v_{co}\right)\\ v_{cn}= v_{co}- \frac{1}{3}\left(v_{ao}+ v_{bo}+ v_{co}\right)\end{array}$
	Line-to-line voltage	$\begin{array}{l}{v}_{ab}= v_{an}- v_{bn}\\ v_{bc}= v_{bn}- v_{cn}\\ v_{ca}= v_{cn}- v_{an}\end{array}$

The equations use these variables.

SFa, SFb, SFc	Phase a, b, c line switching functions, respectively
vbus	Power source bus voltage
Vao, Vbo, Vco	Phase a, b, c line-to-center voltage, respectively
Van, Vbn, Vcn	Phase a, b, c line-to-neutral voltage, respectively
Vab, Vbc, Vca	Phase ab, bc, ca line-to-neutral voltage, respectively
Va_cmd, Vb_cmd, Vc_cmd	Phase a, b, c line-to-neutral voltage commands, respectively

Current and Power Loss

For the line-to-center, line-to-neutral, and line-to-line voltage, the block implements these equations.

Calculation		Equations
Motor and bus power		$\begin{array}{l}{P}_{mtr}= v_{an}{i}_a+v_{bn}{i}_b+v_{cn}{i}_c\\ \\ P_{bus}= v_{bus}{i}_{bus}\end{array}$
Inverter power loss and bus current		$\begin{array}{l}{P}_{in}= P_{bus}= v_{bus}{i}_{bus}\\ \\ P_{out}= P_{mtr}= v_{an}{i}_a+v_{bn}{i}_b+v_{cn}{i}_c+P_{LossInv}\\ \\ i_{bus}= \frac{v_{an}{i}_a+v_{bn}{i}_b+v_{cn}{i}_c+P_{LossInv}}{ v_{bus}}\end{array}$

The equations use these variables.

Pmtr	Power delivered to the motor
Pbus	Power from input bus
Ploss	Power loss
ibus	Power source bus current
ia, ib, ic	Phase a, b, c line current, respectively
Van, Vbn, Vcn	Phase a, b, c line-to-neutral voltage, respectively
vbus	Power source bus voltage

Power Accounting

For the power accounting, the block implements these equations.

Bus Signal			Description	Variable	Equation
PwrInfo	PwrTrnsfrd — Power transferred between blocks Positive signals indicate flow into block Negative signals indicate flow out of block	PwrMtr	Power delivered to the motor	PTrnsfrdMtr	$P_{TrnsfrdMtr}= -(v_{an}{i}_a+v_{bn}{i}_b+v_{cn}{i}_{c })$
		PwrBus	Power from input bus	PTrnsfrdBus	$P_{TrnsfrdBus}= P_{bus}$
	PwrNotTrnsfrd — Power crossing the block boundary, but not transferred Positive signals indicate an input Negative signals indicate a loss	PwrLoss	Power loss Negative value indicates power loss	PNotTrnsfrd	$P_{NotTrnsfrd}= -(P_{TrnsfrdBus}+P_{TrnsfrdMtr})$
	PwrStored — Stored energy rate of change Positive signals indicate an increase Negative signals indicate a decrease		Not used

Lookup Table Memory Optimization

The inverter power loss table parameter Corresponding power loss, ploss_table data is a function of motor torque and motor speed at different battery voltages. Positive current indicates battery discharge. Negative current indicates battery charge.

To enable power loss calculations suitable for code generation targets that limit memory, select Enable memory optimized 2D LUT. The block uses linear interpolation to optimize the inverter power loss lookup table values for code generation. This table summarizes the optimization implementation.

Use Case		Implementation
Motor speed and torque input align with the lookup table breakpoint values.		Memory-optimized power loss is power loss lookup table value at intersection of motor speed and torque.
Motor speed and torque input do not align with the lookup table breakpoint values, but are within range.		Memory-optimized power loss is linear interpolation between corresponding motor speed and torque.
Motor speed and torque input do not align with the lookup table breakpoint values, and are out of range.		Cannot compute a memory-optimized power loss. Block uses extrapolated data.

Extrapolation

The lookup tables optimized for code generation do not support extrapolation for data that is out of range. However, you can include pre-calculated extrapolation values in the power loss lookup table by selecting Specify Extrapolation.

The block uses the endpoint parameters to resize the table data.

User Input	Extrapolation

Ports

Input

PhaseVoltCmd — Phase a, b, c line-to-neutral voltage command

1-by-3 array

Phase a, b, c line-to-neutral voltage command, V_{a_cmd}, V_{b_cmd}, and V_{c_cmd}, in V.

Dependencies

To create this port, set Switching voltage function to Commanded phase voltage.

SwitchCmd — Switch commands

1-by-3 array

Switch commands, S_a, S_b, and S_c, dimensionless.

Dependencies

To create this port, set Switching voltage function to Switch inputs.

BusVolt — Power source bus voltage

bus

Power source bus voltage, V_bus, in V.

PhaseCurr — Phase a, b, c current

1-by-3 array

Phase a, b, c current, i_a, i_b, and i_c, in A.

MtrTrq — Motor torque

scalar

Motor torque, T_mtr, in N·m.

MtrSpd — Motor speed

scalar

Angular speed of the motor, ω_mtr, in rad/s.

InvrtrTemp — Inverter operating temperature

scalar

Inverter operating temperature, Temp_Invrtr, in K.

Dependencies

To create this port, select Input inverter temperature.

Output

Info — Bus signal

bus

The bus signal contains these block calculations.

Signal			Description	Variable	Units
BusCurr			Power source bus current	ibus	A
PwrLossInv			Inverter power loss	εinv	dimensionless
PwrInfo	PwrTrnsfrd	PwrMtr	Power delivered to the motor	PTrnsfrdMtr	W
		PwrBus	Power from input bus	PTrnsfrdBus	W
	PwrNotTrnsfrd	PwrLoss	Power loss	PNotTrnsfrd	W
	PwrStored		Not used

PhaseVolt — Phase a, b, c line-to-neutral voltage

1-by-3 array

Phase a, b, c line-to-neutral voltage, V_an, V_bn, and V_cn, in V.

BusCurr — Power source bus current

scalar

Power source bus current, i_bus, in A.

Parameters

Block Options

Input inverter temperature — Create input port

off (default) | on

Select this parameter to create the InvrtrTemp input port.

The block enables you to specify inverter power loss lookup tables that are functions of motor torque, T_mtr, and motor speed, ω_mtr. If you select Input inverter temperature, the tables are also a function of the inverter temperature, Temp_Invrtr.

Input Inverter Temperature Parameter Setting	Enables Efficiency Table	Function Of
off	Corresponding power loss, ploss_table	ƒ(Tmtr, ωmtr)
on	Corresponding power loss, ploss_table_3d	ƒ(Tmtr, ωmtr, TempInvrtr)

Dependencies

If you select Input inverter temperature to specify a 3D power loss lookup table as a function of motor torque, motor speed, and inverter temperature, you cannot select Enable memory optimized 2D LUT to enable a memory optimization.

Enable memory optimized 2D LUT — Selection

off (default) | on

Enable generation of memory-optimized lookup tables, suitable code generation targets that limit memory.

Dependencies

If you select Enable memory optimized 2D LUT, you cannot select Input inverter temperature.

Calibrate Maps — Calibrate tables with measured data

selection

If you have Model-Based Calibration Toolbox, click Calibrate Maps to virtually calibrate the lookup tables using measured data. The dialog box steps through these tasks.

Task	Description
Import Loss Data	Import this loss data from a file. For example, open <matlabroot>/toolbox/autoblks/autoblksshared/mbctemplates/MappedInverterDataset.xlsx. For more information, see Using Data (Model-Based Calibration Toolbox). Input inverter temperature Setting Required Data off Motor speed, rad/s Motor torque, N·m Power loss, W on Motor speed, rad/s Motor torque, N·m Motor temperature, K Power loss, W Collect inverter data at steady-state operating conditions. Data should cover the inverter speed, torque, and temperature operating range. To filter or edit the data, select Edit in Application. The Model-Based Calibration Toolbox Data Editor opens.
Generate Response Models	Model-Based Calibration Toolbox uses test plans to fit data to Gaussian process models (GPMs). To assess or adjust the response model fit, select Edit in Application. The Model-Based Calibration Toolbox Model Browser opens. For more information, see Model Assessment (Model-Based Calibration Toolbox).
Generate Calibration	Model-Based Calibration Toolbox calibrates the response models and generates calibrated tables. To assess or adjust the calibration, select Edit in Application. The Model-Based Calibration Toolbox CAGE Browser opens. For more information, see Calibration Lookup Tables (Model-Based Calibration Toolbox).
Update block parameters	Update these parameters with the calibration. Input inverter temperature Setting Parameters off Vector of speeds (w) for tabulated losses, w_eff_bp Vector of torques (T) for tabulated losses, T_eff_bp Corresponding power loss, ploss_table on Vector of speeds (w) for tabulated losses, w_eff_bp Vector of torques (T) for tabulated losses, T_eff_bp Vector of temperatures for tabulated losses, Temp_eff_bp Corresponding power loss, ploss_table_3d

Electrical Model

Switching voltage function — Selection

Commanded phase voltage (default) | Switch inputs

Use the Switching voltage function parameter to set the switching voltage function.

Setting	Implementation	Illustration
Commanded phase voltage	Phase a, b, c line-to-neutral voltage command input. Suitable for continuous sinusoidal or space vector modulation input signals.
Switch inputs (default)	Inverter switch input command. Suitable for hardware-in-the-loop (HIL) simulation. The inverter switches S1, S3, and S5 using complemented control for S2, S4, and S6.

Vector of speeds (w) for tabulated losses, w_eff_bp — Speed breakpoints

[-1000 -500 0 500 1000] (default) | 1-by-M vector

Vector of motor speed, ω_mtr, breakpoints for power loss, in rad/s. If you set Enable memory optimized 2D LUT, the block converts the data to single precision.

Resample storage size for w_eff_bp, n1 — Speed bit size

128 (default) | 2 | 4 | 8 | 16 | 32 | 64 | 256

Speed breakpoint storage size, n1, dimensionless. The block resamples the Corresponding power loss, ploss_table data based on the storage size.

Dependencies

To create this parameter, select Enable memory optimized 2D LUT.

Vector of torques (T) for tabulated losses, T_eff_bp — Torque breakpoints

[-200 -100 0 100 200] (default) | 1-by-N vector

Vector of motor torque, T_mtr, breakpoints for power loss, in N·m. If you set Enable memory optimized 2D LUT, the block converts the data to single precision.

Resample storage size for T_eff_bp, n2 — Torque bit size

128 (default) | 2 | 4 | 8 | 16 | 32 | 64 | 256

Torque breakpoint storage size, n2, dimensionless. The block resamples the Corresponding power loss, ploss_table data based on the storage size.

Dependencies

To create this parameter, select Enable memory optimized 2D LUT.

Vector of temperatures for tabulated losses, Temp_eff_bp — Temperature breakpoints

[213.15 293.15 373.15] (default) | 1-by-L vector

Vector of inverter temperature, Temp_Invrtr, breakpoints for power loss, in K.

Dependencies

To create this parameter, select Input inverter temperature.

Corresponding power loss, ploss_table — 2D lookup table

[1 0.999 0.989 0.997 0.996;0.995 0.994 0.993 0.992 0.991;0.990 0.989 0.988 0.987 0.986;0.985 0.984 0.983 0.982 0.981;0.980 0.979 0.978 0.977 0.976] (default) | M-by-N array

Array of values for power loss as a function of M motor speeds, ω_mtr, and N motor torques, T_mtr, in W. Each value specifies the power loss for a specific combination of motor speed and motor torque. The array size must match the dimensions defined by the speed and torque vectors.

If you have Model-Based Calibration Toolbox, click Calibrate Maps to virtually calibrate the lookup table using measured data.

If you set Enable memory optimized 2D LUT, the block converts the data to single precision.

Dependencies

To create this parameter, clear Input inverter temperature.

Corresponding power loss, ploss_table_3d — 3D lookup table

M-by-N-by-L array

Array of values for power loss as a function of M motor speeds, ω_mtr, N motor torques, T_mtr, and L motor temperatures, Temp_Invrtr, in W. Each value specifies the power loss for a specific combination of motor speed, motor torque, and temperature. The array size must match the dimensions defined by the speed, torque, and temperature vectors.

If you have Model-Based Calibration Toolbox, click Calibrate Maps to virtually calibrate the lookup table using measured data.

Dependencies

To create this parameter, select Input inverter temperature.

Specify Extraction

w_eff_bp max endpoint, u1max — Speed breakpoint

1000 (default) | scalar

Speed breakpoint maximum extrapolation endpoint, u1max, in rad/s.

Dependencies

To create this parameter, select Enable memory optimized 2D LUT and Specify Extrapolation.

w_eff_bp min endpoint, u1min — Speed breakpoint

-1000 (default) | scalar

Speed breakpoint minimum extrapolation endpoint, u1min, in rad/s.

Dependencies

To create this parameter, select Enable memory optimized 2D LUT and Specify Extrapolation.

T_eff_bp max endpoint, u2max — Torque breakpoint

200 (default) | scalar

Torque breakpoint maximum extrapolation endpoint, u2max, in rad/s.

Dependencies

To create this parameter, select Enable memory optimized 2D LUT and Specify Extrapolation.

T_eff_bp min endpoint, u2min — Torque breakpoint

-200 (default) | scalar

Torque breakpoint minimum extrapolation endpoint, u2min, in rad/s.

Dependencies

To create this parameter, select Enable memory optimized 2D LUT and Specify Extrapolation.

References

[1] Lee, Byoung-Kuk and Mehrdad Ehsami. “A simplified functional simulation model for three-phase voltage-source inverter using switching function concept.” IEEE^® Transactions on Industrial Electronics, Vol. 48, No. 2, pp. 309-321, April 2001.

[2] Ziogas, Phoivas D., Eduardo P. Wiechmann, and Victor R. Stefanovic. “A Computer-Aided Analysis and Design Approach for Static Voltage Source Inverters.” IEEE Transactions on Industrial Electronics Transactions on Industry Applications, Vol. IA-21, No. 5, September/October 1985.

Extended Capabilities

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

Version History

Introduced in R2019a