Threephase voltage source inverter
Powertrain Blockset / Propulsion / Electric Motors and Inverters
The ThreePhase Voltage Source Inverter block implements a threephase voltage source inverter that generates neutral voltage commands for a balanced threephase load. Configure the voltage switching function for continuous vector modulation or inverter switch input signals. You can incorporate the block into a closedloop 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 linetoneutral voltage command input. Suitable for continuous sinusoidal or space vector modulation input signals. 

Switch inputs (default) 
Inverter switch input command. Suitable for hardwareintheloop (HIL) simulation. The inverter switches S1, S3, and S5 using complimented control for S2, S4, and S6. 

If you have ModelBased 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
For more information, see Using Data (ModelBased Calibration Toolbox).
Collect inverter data at steadystate operating conditions. Data should cover the inverter speed, torque, and temperature operating range. To filter or edit the data, select Edit in Application. The ModelBased Calibration Toolbox Data Editor opens.  
Generate Response Models  ModelBased 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 ModelBased Calibration Toolbox Model Browser opens. For more information, see Model Assessment (ModelBased Calibration Toolbox).  
Generate Calibration  ModelBased Calibration Toolbox calibrates the response models and generates calibrated tables. To assess or adjust the calibration, select Edit in Application. The ModelBased Calibration Toolbox CAGE Browser opens. For more information, see Calibration Tables (ModelBased Calibration Toolbox).  
Update block parameters  Update these parameters with the calibration.

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

Commanded phase
voltage  Continuous linetoneutral voltage commands set to phase a, b, c linetoneutral voltage command input  $$\begin{array}{l}{v}_{an}={v}_{a\_cmd}\\ {v}_{bn}={v}_{b\_cmd}\\ {v}_{cn}={v}_{c\_cmd}\end{array}$$ 
Linetoline 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  $$\begin{array}{l}S{F}_{a}=\{\begin{array}{c}1\text{S}1\text{onandS2off}\\ 1\text{S}1\text{offandS2on}\end{array}\\ \\ S{F}_{b}=\{\begin{array}{c}1\text{S}3\text{onandS4off}\\ 1\text{S}3\text{offandS4on}\end{array}\\ \\ S{F}_{c}=\{\begin{array}{c}1\text{S}5\text{onandS6off}\\ 1\text{S}5\text{offandS6on}\end{array}\end{array}$$ 
Linetocenter point voltage  $$\begin{array}{l}{v}_{ao}=\frac{{v}_{bus}}{2}S{F}_{a}\\ {v}_{bo}=\frac{{v}_{bus}}{2}S{F}_{b}\\ {v}_{co}=\frac{{v}_{bus}}{2}S{F}_{c}\end{array}$$  
Linetoneutral voltage  $\begin{array}{l}{v}_{an}={v}_{ao}{v}_{no}\\ {v}_{bn}={v}_{bo}{v}_{no}\\ {v}_{cn}={v}_{co}{v}_{no}\\ \\ {v}_{an}+{v}_{bn}+{v}_{cn}=0\\ \\ {v}_{no}=\frac{1}{3}\left({v}_{ao}+{v}_{bo}+{v}_{co}\right)\\ \\ {v}_{an}={v}_{ao}\frac{1}{3}\left({v}_{ao}+{v}_{bo}+{v}_{co}\right)\\ {v}_{bn}={v}_{bo}\frac{1}{3}\left({v}_{ao}+{v}_{bo}+{v}_{co}\right)\\ {v}_{cn}={v}_{co}\frac{1}{3}\left({v}_{ao}+{v}_{bo}+{v}_{co}\right)\end{array}$  
Linetoline 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.
SF_{a}, SF_{b}, SF_{c}  Phase a, b, c line switching functions, respectively 
v_{bus}  Power source bus voltage 
V_{ao}, V_{bo}, V_{co}  Phase a, b, c linetocenter voltage, respectively 
V_{an}, V_{bn}, V_{cn}  Phase a, b, c linetoneutral voltage, respectively 
V_{ab}, V_{bc}, V_{ca}  Phase ab, bc, ca linetoneutral voltage, respectively 
V_{a_cmd}, V_{b_cmd}, V_{c_cmd}  Phase a, b, c linetoneutral voltage commands, respectively 
For the linetocenter, linetoneutral, and linetoline 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.
P_{mtr}  Power delivered to the motor 
P_{bus}  Power from input bus 
P_{loss}  Power loss 
i_{bus}  Power source bus current 
i_{a}, i_{b}, i_{c}  Phase a, b, c line current, respectively 
V_{an}, V_{bn}, V_{cn}  Phase a, b, c linetoneutral voltage, respectively 
v_{bus}  Power source bus voltage 
For the power accounting, the block implements these equations.
Bus Signal  Description  Variable  Equation  



 Power delivered to the motor  P_{TrnsfrdMtr}  ${P}_{TrnsfrdMtr}=({v}_{an}{i}_{a}+{v}_{bn}{i}_{b}+{v}_{cn}{i}_{c})$ 
PwrBus  Power from input bus  P_{TrnsfrdBus}  ${P}_{TrnsfrdBus}={P}_{bus}$  
 PwrLoss  Power loss Negative value indicates power loss  P_{NotTrnsfrd}  ${P}_{NotTrnsfrd}=({P}_{TrnsfrdBus}+{P}_{TrnsfrdMtr})$  
 Not used 
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.  Memoryoptimized 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.  Memoryoptimized 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 memoryoptimized power loss. Block uses extrapolated data. 
The lookup tables optimized for code generation do not support extrapolation for data that is out of range. However, you can include precalculated 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 

[1] Lee, ByoungKuk and Mehrdad Ehsami. “A simplified functional simulation model for threephase voltagesource inverter using switching function concept.” IEEE^{®} Transactions on Industrial Electronics, Vol. 48, No. 2, pp. 309321, April 2001.
[2] Ziogas, Phoivas D., Eduardo P. Wiechmann, and Victor R. Stefanovic. “A ComputerAided Analysis and Design Approach for Static Voltage Source Inverters.” IEEE Transactions on Industry Applications, Vol. IA21, No. 5, September/October 1985.