# Inverter (Three-Phase)

Implements a three-phase inverter model for AC Motor Drives

## Library

Simscape / Electrical / Specialized Power Systems / Electric Drives / Fundamental Drive Blocks

• ## Description

The Inverter (Three-Phase) block models a standard three-leg, two-level inverter model (detailed mode) or an average-value inverter model (average mode). Average mode has multiple instances, depending on the AC motor drive type.

### Detailed mode

In detailed mode, the Inverter (Three-Phase) block is an instance of the Universal Bridge block configured as a three-arm (three-phase), forced-commutated converter.

### Average Mode

In average mode, the Inverter (Three-Phase) block implements an average-value inverter model for a specific AC drive type. The average-value inverter model can be a current source type with AC current reference signal, voltage source type with an AC voltage reference signal, or voltage source type with AC current reference signal.

Current Source Type with AC Current Reference Signal

This model is used for an AC drive type based on field-oriented control, WFSM vector control, or PMSM vector control.

The inverter is represented by current sources on the AC side during normal operation. The AC current reference signal generates the three-phase currents at the inverter output. When the inverter is saturated, it operates in square-wave mode, and the current sources are replaced with voltage sources. The average-value inverter model of this type is shown in the figure. The model is composed of one controlled current source on the DC side and of two controlled current sources and three controlled voltage sources on the AC side. The DC current source allows the representation of the average DC bus current behavior following the equation

Idc = (Pac + Plosses) / Vdc,

with Pac being the AC side instantaneous power, Plosses the losses in the power electronics devices, and Vdc the DC bus voltage.

On the AC side, the current sources represent the average phase currents fed to the motor. The current values are set equal to the current references sent by the current regulator. A small current is injected to compensate for the current drawn by the three-phase load (needed because of the inverter current sources in series with the inductive motor).

The currents are fed by three controlled voltage sources during loss of current tracking due to insufficient inverter voltage. These voltage sources represent the square wave mode and allow good representation of the phase currents during inverter saturation. Each voltage source outputs either Vin or 0, depending on the values of the pulses (1 or 0) send by the current controller. This mode of operation is detected from the Saturation detection block using the DC bus voltage and the counter electro-motive force generated by the AC machine.

Voltage Source Type with AC Voltage Reference Signal

This model is used for AC drive type based on space vector modulation.

The inverter is represented with voltage sources on the AC side. The AC voltage reference signal generates the three-phase voltage at the inverter output. The average-value inverter model of this type is shown in the figure. The model is composed of one controlled current source on the DC side and three controlled voltage sources on the AC side. The DC current source allows the representation of the average DC bus current behavior, following the equation

Idc = αaIa + αbIb + αcIc,

with αa, αb, αc being the PWM duty cycles (or phase-voltage-to-DC-bus-voltage ratio) of the inverter legs A, B, and C respectively, and Ia, Ib, Ic the corresponding three-phase currents. The three AC voltage sources represent the average voltage values of the three-phase inverter voltages Va, Vb, Vc, following the equation

Va = αaVin

Vb = αbVin

Vc = αcVin,

with Vin being the input DC bus voltage value.

Voltage Source Type with AC Current Reference Signal

This average-value inverter model is used for the Brushless DC current control AC drive type.

The inverter is represented with voltage sources on the AC side. The AC machine parameters are required together with the AC current reference signal to generate the three-phase voltages at the inverter output. The figure shows the average-value inverter model of this type for a trapezoidal PMSM drive. The model is composed of one controlled current source on the DC side and two controlled voltage sources on the AC side. The DC current source allows the representation of the DC bus current behavior described by the equation

Idc = (Pout + Plosses) / Vin,

with Pout being the output AC power, Plosses the losses in the power electronic devices, and Vin the DC bus voltage.

On the AC side, the voltage sources are fed by the instantaneous voltages provided by the Trapezoidal PMSM dynamic model (see the PMSM documentation for the machine model). This dynamic model takes the AC reference currents (the rate of these currents has been limited to represent the real-life currents), the measured BEMF voltages, and the machine speed to compute the terminal voltages to apply to the machine.

The dynamic rate limiter limits the rate of the reference currents when transitions occur. The rate depends on the inverter saturation degree.

During loss of current tracking due to insufficient inverter voltage, the dynamic rate limiter saturates the reference current according to this operation mode.

## Parameters

Model detail level

Specify the model detail level to use:

• `Detailed` (default)

• `Average`

Sample Time

The sample time of the inverter, in seconds. The default value is `2e-6`.

Snubber resistance Rs (Ohms)

The snubber resistance, in ohms. Set the Snubber resistance Rs parameter to `inf` to eliminate the snubbers from the model. The default value is `10e3`.

Snubber capacitance Cs (F)

The snubber capacitance, in farads. Set the Snubber capacitance Cs parameter to `0` to eliminate the snubbers or to `inf` to get a resistive snubber. The default value is `inf`.

Power electronic device

Select the type of power electronic device to use in the bridge.

• `GTO / Diodes` (default)

• `MOSFET / Diodes`

• `IGBT / Diodes`

Drive type

Specify the drive type to use. This parameter is visible only when the Model detail level parameter is set to `Average`. Select one of these values:

• `Field-oriented control` (default)

• `Space vector modulation`

• `WFSM vector control`

• `PMSM vector control`

• `Brushless DC`

Ron (Ohms)

Internal resistance of the switch, in ohms. The default value is `1e-3`.

Forward voltages (V) [Vf, Vfd]

Forward voltages, in volts, of the forced-commutated devices (GTO, MOSFET, or IGBT) and of the antiparallel diodes. This parameter is available when the selected Power electronic device is `GTO/Diodes` or `IGBT/Diodes`. The default value is `[1.2,1.2]`.

Fall time and tail time (s) [Tf, Tt]

Fall time Tf and tail time Tt, in seconds, for the GTO or the IGBT devices. The default value is `[1e-6,2e-6]`.

The default value is`[1e-6,2e-6]`.

Measurements

Default is `None`.

Select `Device voltages` to measure the voltages across the six power electronic device terminals.

Select `Device currents` to measure the currents flowing through the six power electronic devices. If antiparallel diodes are used, the measured current is the total current in the forced-commutated device (GTO, MOSFET, or IGBT) and in the antiparallel diode. A positive current therefore indicates a current flowing in the forced-commutated device and a negative current indicates a current flowing in the diode. If snubber devices are defined, the measured currents are the ones flowing through the power electronic devices only.

Select `UAB UBC UCA UDC voltages` to measure the terminal voltages (AC and DC) of the Inverter (Three-Phase) block.

Select `All voltages and currents` to measure all voltages and currents defined for the Inverter (Three-Phase) block.

Place a Multimeter block in your model to display the selected measurements during the simulation. In the Available Measurements menu of the Multimeter block, the measurement is identified by a label followed by the block name.

Measurement

Label

Device voltages

`Usw1:`

Branch current

`Isw1:`

Terminal voltages

`Uab:`

Source Frequency (Hz)

Synchronous frequency of the machine, in hertz. This parameter is visible only when the Model detail level parameter is set to `Average`. The default value is `60`.

Reference frame

Specifies the reference frame that is used to convert input voltages (abc reference frame) to the dq reference frame, and output currents (dq reference frame) to the abc reference frame. You can choose from the following reference frame transformations:

• `Rotor` (default)

• `Stationary`

• `Synchronous`

This parameter is visible only when the Model detail level parameter is set to `Average` and the Drive type parameter is set to ```Field-oriented control```.

Stator [Rs (Ohms), Lls (H)]

The stator resistance, in ohms, and leakage inductance, in henry, of the motor. This parameter is visible only when the Model detail level parameter is set to `Average` and the Drive type parameter is set to ```Field-oriented control``` .The default value is `[14.85e-3,0.3027e-3]`.

Stator [Rs (Ohms), Ll, Lmd, Lmq (H)]

The stator resistance, in ohms, leakage inductance, in henry, and the d and q mutual inductances of the motor, in henry. This parameter is visible only when the Model detail level parameter is set to `Average` and the Drive type parameter is set to `WFSM vector control`. The default value is `[2.01e-3,4.289e-4,4.477e-3,1.354e-3]`.

Rotor [ Rr' (Ohms) Llr' (H)]

The rotor resistance, in ohms, and leakage inductance, in henry, both referred to the stator. This parameter is visible only when the Model detail level parameter is set to `Average` and the Drive type parameter is set to ```Field-oriented control```. The default value is `[9.295e-3,0.3027e-3]`.

Mutual inductance Lm (H)

The magnetizing inductance of the motor, in henry. This parameter is visible only when the Model detail level parameter is set to `Average` and the Drive type parameter is set to `Field-oriented control`. The default value is `10.46e-3`.

The default value is`10.46e-3`.

Inductances (H) [Ld, Lq]

The phase-to-neutral Ld and Lq inductances in the d-axis and q-axis of the sinusoidal model with salient-pole rotor. This parameter is visible only when the Model detail level parameter is set to `Average` and the Drive type parameter is set to `PMSM vector control`.

The default value is `[8.5e-3,8.5e-3]`.

Inductance (H)

The armature inductance of the sinusoidal model with round rotor (Ld is equal to Lq). This parameter is visible only when the Model detail level parameter is set to `Average` and the Drive type parameter is set to ```Brushless DC``` . The default value is `8.5e-3`.

Resistance (Ohms)

The stator phase resistance Rs, in ohms, of the motor. This parameter is visible only when the Model detail level parameter is set to `Average` and the Drive type parameter is set to `PMSM vector control`. The default value is `0.2`.

Flux induced by magnets (Wb)

The constant flux, in weber, per pole pairs induced in the stator windings by the magnets of the motor. This parameter is visible only when the Model detail level parameter is set to `Average` and the Drive type parameter is set to `PMSM vector control` or ```Brushless DC```. The default value is `0.175`.

Pairs of poles

The number of pole pairs of the machine controlled by the inverter. This parameter is visible only when the Model detail level parameter is set to `Average`. The default value is `4`.

## Inputs and Outputs

`g`

The gate input for the controlled switch devices. Pulses are sent to upper and lower switches of inverter legs A, B, and C. This input is visible only when the Model detail level parameter is set to `Detailed`.

`ctrl`

Control signals from the appropriate controller. In average mode, the Inverter (Three-Phase) block no longer receives pulses, but receives various types of other signals that are drive-type specific. This input is visible only when the Model detail level parameter is set to `Average` and the Drive type parameter is set to ```Field-oriented control```, `WFSM vector control`, or `PMSM vector control`.

`Duty`

The PWM duty cycles (or phase-voltage-to-DC-bus-voltage ratio) of the inverter legs A, B, and C. This input is visible only when the Model detail level parameter is set to `Average` and the Drive type parameter is set to ```Space vector modulation```.

`+`

The positive terminal on the DC side.

`-`

The negative terminal on the DC side.

`A, B, C`

The three-phase terminals on the AC side.

## Examples

The Inverter (Three-Phase) block is used in the AC1 to AC7 blocks of the Electric Drives library.

 Bose, B. K. Modern Power Electronics and AC Drives, NJ: Prentice-Hall, 2002.

 Erickson, R. W., and D. Maksimovic. Fundamentals of Power Electronics, Second Edition. NY: Kluwer Academic Publishers, 2004.