# Space Vector PWM VSI Induction Motor Drive

Implement space vector PWM VSI induction motor drive

## Library

Electric Drives/AC drives

## Description

The high-level schematic shown below is built from six main blocks. The induction motor, the three-phase inverter, and the three-phase diode rectifier models are provided with the SimPowerSystems™ library. More details are available in the reference pages for these blocks. The speed controller, the braking chopper, and the space vector modulator models are specific to the drive library. It is possible to use a simplified version of the drive containing an average-value model of the inverter for faster simulation.

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

## Speed Controller

The speed controller is based on a PI regulator that controls the motor slip. As shown in the following figure, the slip value computed by the PI regulator is added to the motor speed in order to produce the demanded inverter frequency. The latter frequency is also used to generate the demanded inverter voltage in order to maintain the motor V/F ratio constant.

## Space Vector Modulator

The space vector modulator (SVM) contains seven blocks, shown in the following figure. These blocks are described below.

The three-phase generator is used to produce three sine waves with variable frequency and amplitude. The three signals are out of phase with each other by 120 degrees. The inverter demanded frequency and voltage are two of the block inputs.

The low-pass bus filter is used to remove fast transients from the DC bus voltage measurement. This measure is used to compute the voltage vector applied to the motor.

The alpha beta transformation converts variables from the three-phase system to the two-phase αβ system.

The αβ vector sector is used to find the sector of the αβ plane in which the voltage vector lies. The αβ plane is divided into six different sectors spaced by 60 degrees.

The ramp generator is used to produce a unitary ramp at the PWM switching frequency. This ramp is used as a time base for the switching sequence.

The switching time calculator is used to calculate the timing of the voltage vector applied to the motor. The block input is the sector in which the voltage vector lies.

The gates logic receives the timing sequence from the switching time calculator and the ramp from the ramp generator. This block compares the ramp and the gate timing signals to activate the inverter switches at the proper time.

When using the average-value inverter, the gates logic block is disabled and the inverter leg PWM duty cycles are issued by the switching time calculator to control the average-value inverter.

## Average-Value Inverter

The average-value inverter is shown in the following figure.

It 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 next equation:

Idc = αaIa + αbIb + αcIc

with αa, αb, αc being the PWM duty cycles 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 next equation:

Va = αaVin
Vb = αbVin
Vc = αcVin,

with Vin being the input DC bus voltage value.

## Braking Chopper

The braking chopper block contains the DC bus capacitor and the dynamic braking chopper, which is used to absorb the energy produced by a motor deceleration.

## Remarks

The model is discrete. Good simulation results have been obtained with a 2 µs time step. In order to simulate a digital controller device, the control system has two different sampling times:

• The speed controller sampling time

• The SVM controller sampling time

The speed controller sampling time has to be a multiple of the SVM 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.

In the AC2 motor drive, the motor speed is regulated by controlling the motor slip. The motor current or torque is not regulated, however, so the speed response tends to be sluggish at low speed because of torque ripple.

When reversing speed, a short delay is required at the zero speed crossing so that air gap flux decays to zero.

## 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.

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.

### Converters and DC Bus Tab

Rectifier section

The rectifier section of the Converters and DC bus tab displays the parameters of the Universal Bridge block of the Fundamental Blocks (powerlib) library. Refer to the Universal Bridge for more information on the universal bridge parameters.

Inverter section

The inverter section of the Converters and DC bus tab displays the parameters of the Universal Brige block of the Fundamental Blocks (powerlib) library. Refer to the Universal Bridge for more information on the universal bridge parameters. This parameter is not used when using the average-value inverter.

### Braking Chopper section

Capacitance

The DC bus capacitance (F).

Resistance

The braking chopper resistance used to avoid bus over-voltage during motor deceleration or when the load torque tends to accelerate the motor (Ω).

Frequency

The braking chopper frequency (Hz).

Activation and Shutdown Voltage

The dynamic braking is activated when the bus voltage reaches the upper limit of the hysteresis band. The dynamic braking is shut down when the bus voltage reaches the lower limit of the hysteresis band. The following figure illustrates the braking hysteresis logic.

### Controller Tab

Schematic Button

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

### Speed Controller section

Speed Ramps — Acceleration

The maximum change of speed allowed during motor acceleration. An excessively large positive value can cause DC bus under-voltage (rpm/s).

Speed Ramps — Deceleration

The maximum change of speed allowed during motor deceleration. An excessively large negative value can cause DC bus over-voltage (rpm/s).

Proportional Gain

The speed controller proportional gain.

Integral Gain

The speed controller integral gain.

Output Negative Saturation

The maximum negative slip compensation computed by the slip regulator (Hz).

Output Positive Saturation

The maximum positive slip compensation computed by the slip regulator (Hz).

Minimum Frequency

The minimum demanded inverter frequency applied to the motor (Hz).

Maximum Frequency

The maximum demanded inverter frequency applied to the motor (Hz).

Minimum Output Voltage

The minimum demanded inverter output voltage (V). If this parameter is set to zero, the zero speed cannot be reached under several load conditions.

Maximum Output Voltage

The maximum demanded inverter output voltage (V). This parameter must be set in accordance with the motor rating. If this parameter is set too high, you will observe over-modulation in the current and voltage waveforms.

Volts / Hertz Ratio

The proportionality constant between the stator line-to-line RMS voltage and frequency (V / Hz).

Zero Speed Crossing Time

The delay at zero speed to eliminate the motor air gap residual flux (s).

Speed Sensor Cutoff Frequency

The speed measurement first-order low-pass filter cutoff frequency (Hz).

Sampling Time

The speed controller sampling time(s). The sampling time must be a multiple of the simulation time step.

### SVM Generator section

Switching Frequency

The inverter switching frequency (Hz).

Voltage Sensor Cutoff Frequency

The cutoff frequency of the first-order low-pass filter applied to the DC bus voltage measurement.(Hz).

Sampling Time

The SVM generator sampling time (s). The sampling time must be a multiple of the simulation time step.

## 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.