# Space Vector PWM VSI Induction Motor Drive

Implement space vector PWM VSI induction motor drive

## Library

Electric Drives/AC drives

## Description

The Space Vector PWM VSI Induction Motor Drive block represents a classical closed-loop Volts/Hz control drive for induction motors. The block contains a closed-loop speed control with slip regulation. The speed-control loop outputs the reference motor slip, which is added to the measured rotor speed to obtain the reference frequency of the stator flux. The reference stator voltage is derived from the Volts/Hz control and from the constant flux strategy. The stator frequency and voltage references are then used to obtain the required PWM signals for the inverter following the space vector modulation strategy.

The main advantage of this drive compared to vector-controlled drives is its implementation simplicity. However, as with most scalar-controlled drives, the dynamic response of this drive is slow due to the inherent coupling effect between the torque and flux present in the machine.

 Note   In Simscape™ Power Systems™ software, the Space Vector PWM VSI Induction Motor Drive block is commonly called the `AC2` motor drive.

## High-Level Schematic

The Space Vector PWM VSI Induction Motor Drive block uses the following blocks from the Electric Drives / Fundamental Drive Blocks library:

• Speed Controller (Scalar Control)

• Space Vector Modulator

• DC Bus

• Inverter (Three-Phase)

## Remarks

The model is discrete. Good simulation results have been obtained with a 2 µs time step. The control system has two different sampling times:

• The speed controller sampling time

• The space vector modulator controller sampling time

The speed controller sampling time has to be a multiple of the space vector modulator sampling time. The latter sampling time has to be a multiple of the simulation time step.

The simulation step size must be chosen in accordance with the inverter's switching frequency. A rule of thumb is to choose a simulation step size 100 times smaller than the switching period. If the simulation step size is set too high, the simulation results can be erroneous. The average-value inverter allows the use of bigger simulation time steps since it does not generate small time constants (due to the RC snubbers) inherent to the detailed converter. For a controller sampling time of 20 µs, good simulation results have been obtained for a simulation time step of 20 µs. This time step can, of course, not be higher than the controller time step.

## Dialog Box

### Asynchronous Machine Tab

The Asynchronous Machine tab displays the parameters of the Asynchronous Machine block of the Fundamental Blocks (powerlib) library.

Output bus mode

Select how the output variables are organized. If you select Multiple output buses, the block has three separate output buses for motor, converter, and controller variables. If you select Single output bus, all variables output on a single bus.

Model detail level

Select between the detailed and the average-value inverter.

Mechanical input

Select between the load torque, the motor speed and the mechanical rotational port as mechanical input. If you select and apply a load torque, the output is the motor speed according to the following differential equation that describes the mechanical system dynamics:

`${T}_{e}=J\frac{d}{dt}{\omega }_{r}+F{\omega }_{r}+{T}_{m}$`

This mechanical system is included in the motor model.

For the mechanical rotational port, the connection port S counts for the mechanical input and output. It allows a direct connection to the Simscape environment. The mechanical system of the motor is also included in the drive and is based on the same differential equation.

If you select the motor speed as mechanical input, then you get the electromagnetic torque as output, allowing you to represent externally the mechanical system dynamics. The internal mechanical system is not used with this mechanical input selection and the inertia and viscous friction parameters are not displayed.

### Converters and DC Bus Tab

The Converters and DC bus tab displays the parameters of the Universal Bridge block (diode bridge configuration) of the Fundamental Blocks / Power Electronics library as well as the DC Bus and Inverter (Three-Phase) blocks of the Electric Drives / Fundamental Drive Blocks library.

### Controller Tab

The Controller tab displays the parameters of the Speed Controller (Scalar Control) and Space Vector Modulator blocks of the Electric Drives / Fundamental Drive Blocks library.

Schematic Button

When you press this button, a diagram illustrating the speed and current controllers schematics appears.

## Block Inputs and Outputs

`SP`

The speed or torque set point. The speed set point can be a step function, but the speed change rate will follow the acceleration / deceleration ramps. If the load torque and the speed have opposite signs, the accelerating torque will be the sum of the electromagnetic and load torques.

`Tm` or `Wm`

The mechanical input: load torque (Tm) or motor speed (Wm). For the mechanical rotational port (S), this input is deleted.

`A, B, C `

The three phase terminals of the motor drive.

`Wm`, `Te` or `S`

The mechanical output: motor speed (Wm), electromagnetic torque (Te) or mechanical rotational port (S).

When the Output bus mode parameter is set to Multiple output buses, the block has the following three output buses:

`Motor`

The motor measurement vector. This vector allows you to observe the motor's variables using the Bus Selector block.

`Conv`

The three-phase converters measurement vector. This vector contains:

• The DC bus voltage

• The rectifier output current

• The inverter input current

Note that all current and voltage values of the bridges can be visualized with the Multimeter block.

`Ctrl`

The controller measurement vector. This vector contains:

• The slip compensation

• The speed error (difference between the speed reference ramp and actual speed)

• The speed reference ramp

When the Output bus mode parameter is set to Single output bus, the block groups the Motor, Conv, and Ctrl outputs into a single bus output.

## Model Specifications

The library contains a 3 hp and a 200 hp drive parameter set. The specifications of these two drives are shown in the following table.

3 HP and 200 HP Drive Specifications

3 HP Drive

200 HP Drive

Drive Input Voltage

Amplitude

220 V

575 V

Frequency

60 Hz

60 Hz

Motor Nominal Values

Power

3 hp

200 hp

Speed

1705 rpm

1785 rpm

Voltage

220 V

575 V

## Example

The `ac2_example` example illustrates an AC2 induction motor drive simulation with standard load conditions. At time t = 0 s, the speed set point is 1000 rpm.

As shown in the following figure, the speed precisely follows the acceleration ramp. At t = 0.5 s, the nominal load torque is applied to the motor. At t = 1 s, the speed set point is changed to 1500 rpm. The speed increases to 1500 rpm. At t = 1.5 s, the mechanical load passes from 11 N.m to −11 N.m. The figure illustrates the results obtained respectively with the detailed and the average-value inverter. Average voltage, current, torque, and speed values are identical for both models. The higher frequency signal components are not represented with the average-value converter.

AC2 Example Waveforms (Blue : Detailed Converter, Red : Average-Value Converter)

## References

[1] Bose, B. K., Modern Power Electronics and AC Drives, Prentice-Hall, N.J., 2002.

[2] Grelet, G., and G. Clerc, Actionneurs électriques, Éditions, Eyrolles, Paris, 1997.

[3] Krause, P. C, Analysis of Electric Machinery, McGraw-Hill, 1986.