# DTC Induction Motor Drive

Implement direct torque and flux control (DTC) induction motor drive model

## 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 Simscape™ Power Systems™ library. More details on these three blocks are available in the reference sections of each block. The speed controller, the braking chopper, and the DTC controller models are specific to the drive library.

 Note   In Simscape Power Systems software, the DTC Induction Motor Drive block is commonly called the `AC4` motor drive.

## Speed Controller

The speed controller is based on a PI regulator, shown below. The output of this regulator is a torque set point applied to the DTC controller block.

## DTFC Controller

The Direct Torque and Flux Control (DTFC) controller contains five main blocks, shown below. These blocks are described below.

The Torque & Flux calculator block is used to estimate the motor flux αβ components and the electromagnetic torque. This calculator is based on motor equation synthesis.

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

The Flux & Torque Hysteresis blocks contain a two-level hysteresis comparator for flux control and a three-level hysteresis comparator for the torque control. The description of the hysteresis comparators is available below.

The Switching table block contains two lookup tables that select a specific voltage vector in accordance with the output of the Flux & Torque Hysteresis comparators. This block also produces the initial flux in the machine.

The Switching control block is used to limit the inverter commutation frequency to a maximum value specified by the user.

## 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 D.T.C. controller sampling time

The speed controller sampling time has to be a multiple of the D.T.C. sampling time. The latter sampling time has to be a multiple of the simulation time step.

## Dialog Box

### Asynchronous Machine Tab

The Aynchronous Machine tab displays the parameters of the Aynchronous 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.

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.

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 rectifier block of the Fundamental Blocks (powerlib) library. Refer to the Universal Bridge for more information on the rectifier parameters.

Inverter Section

The inverter section of the Converters and DC Bus tab displays the parameters of the Inverter block of the Fundamental Blocks (powerlib) library. Refer to the Universal Bridge for more information on the inverter parameters.

DC-Bus Capacitance

The DC bus capacitance (F).

Braking Chopper section: 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).

Braking Chopper section: Frequency

The braking chopper frequency (Hz).

Braking Chopper section: Activation Voltage

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

Braking Chopper section: Shutdown Voltage

The dynamic braking is shut down when the bus voltage reaches the lower limit of the hysteresis band. The Chopper hysteresis logic is shown below:

### Controller Tab

Regulation type

This parameter allows you to choose between speed and torque regulation.

Schematic

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

#### Speed Controller section

Speed cutoff frequency

The speed measurement first-order low-pass filter cutoff frequency (Hz). This parameter is used in speed regulation mode only.

Speed controller sampling time

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

Speed Ramps — Acceleration

The maximum change of speed allowed during motor acceleration (rpm/s). An excessively large positive value can cause DC bus under-voltage. This parameter is used in speed regulation mode only.

Speed Ramps — Deceleration

The maximum change of speed allowed during motor deceleration (rpm/s). An excessively large negative value can cause DC bus overvoltage. This parameter is used in speed regulation mode only.

PI Regulator — Proportional Gain

The speed controller proportional gain. This parameter is used in speed regulation mode only.

PI Regulator — Integral Gain

The speed controller integral gain. This parameter is used in speed regulation mode only.

Torque output limits — Negative

The maximum negative demanded torque applied to the motor by the current controller (N.m).

Torque output limits — Positive

The maximum positive demanded torque applied to the motor by the current controller (N.m).

#### DTC Controller Section

Maximum switching frequency

The maximum inverter switching frequency (Hz).

Initial machine flux

The desired initial stator flux established before the DTC drive module begins to produce an electromagnetic torque. This flux is produced by applying a constant voltage vector at the motor terminals (Wb).

DTC sampling time

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

Hysteresis bandwidth — Torque

The torque hysteresis bandwidth. This value is the total bandwidth distributed symmetrically around the torque set point (N.m). The following figure illustrates a case where the torque set point is Te* and the torque hysteresis bandwidth is set to dTe.

Hysteresis bandwidth — Flux

The stator flux hysteresis bandwidth. This value is the total bandwidth distributed symmetrically around the flux set point (Wb). The following figure illustrates a case where the flux set point is ψ* and the torque hysteresis bandwidth is set to dψ.

 Note   This bandwidth can be exceeded because a fixed-step simulation is used. A rate transition block is needed to transfer data between different sampling rates. This block causes a delay in the gate signals, so the current may exceed the hysteresis band.

## 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 torque reference

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

• The speed reference ramp or torque reference

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.

Drive Specifications

3 HP Drive

200 HP Drive

Drive Input Voltage

Amplitude

220 V

460 V

Frequency

60 Hz

60 Hz

Motor Nominal Values

Power

3 hp

200 hp

Speed

1705 rpm

1785 rpm

Voltage

220 V

460 V

## Example

The `ac4_example` example illustrates the simulation of an AC4 motor drive with standard load condition.

At time t = 0 s, the speed set point is 500 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 0 rpm. The speed decreases to 0 rpm. At t = 1.5 s., the mechanical load passes from 792 N.m to −792 N.m.

## 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.