# Brushless DC Motor Drive

Implement brushless DC motor drive using Permanent Magnet Synchronous Motor (PMSM) with trapezoidal back electromotive force (BEMF)

## Library

Electric Drives/AC drives

## Description

The Brushless DC Motor Drive (AC7) block represents a standard current-controlled drive for brushless DC (BLDC) motors. The BLDC motors are also known as permanent magnet synchronous motors with trapezoidal back EMF. This drive features closed-loop speed control through stator current control, using Hall sensors. The speed control loop outputs the reference electromagnetic torque of the machine. The reference stator phase currents corresponding to the commanded torque are derived based on the machine torque constant and the Hall sensor signals. The reference phase currents are then used to obtain the required gate signals for the inverter through a hysteresis-band current controller.

The main advantage of this drive compared to voltage-controlled, PWM inverter BLDC drives, is its smooth dynamic response. This drive provides inherent current/torque-limiting capability during motor startup and acceleration. However, to operate properly, the drive requires a close-loop torque control based on machine currents signals.

### Note

In Simscape™ Power Systems™ software, the Brushless DC Motor Drive block is commonly called the `AC7` motor drive.

The Brushless DC Motor Drive block uses these blocks from the Electric Drives / Fundamental Drive Blocks library:

• Speed Controller (AC)

• Current Controller (Brushless DC)

• DC Bus

• Inverter (Three-Phase)

## Remarks

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

• Speed controller sampling time

• Current controller sampling time

The speed controller sampling time has to be a multiple of the current controller sampling time. The latter sampling time has to be a multiple of the simulation time step. 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 current controller sampling time of 40 µs, good simulation results have been obtained for a simulation time step of 40 µs. The simulation time step cannot be higher than the current controller time step.

## Parameters

### General

Output bus mode

Select how the output variables are organized. If you select ```Multiple output buses``` (default), 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. Default is `Detailed`.

Mechanical input

Select between the load torque, the motor speed and the mechanical rotational port as mechanical input. Default is ```Torque Tm```.

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.

Use signal names as labels

When you select this check box, the `Motor`, `Conv`, and `Ctrl` measurement outputs use the signal names to identify the bus labels. Select this option for applications that require bus signal labels to have only alphanumeric characters.

When this check box is cleared (default), the measurement output uses the signal definition to identify the bus labels. The labels contain nonalphanumeric characters that are incompatible with some Simulink® applications.

### Permanent Magnet Synchronous Machine Tab

The Permanent Magnet Synchronous Machine tab displays the parameters of the Permanent Magnet Synchronous Machine block of the Fundamental Blocks (powerlib) library.

### 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. For more information on the Universal Bridge parameters, refer to the Universal Bridge reference page.

#### DC Bus Section

Capacitance

The DC bus capacitance (F). Default is `2000e-6`.

#### 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 (ohms). Default is `8`.

Chopper frequency

The braking chopper frequency (Hz). Default is `4000`.

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. Default is `320`.

Shutdown voltage

The dynamic braking is shut down when the bus voltage reaches the lower limit of the hysteresis band. Default is `310`. The chopper hysteresis logic is shown in the following figure.

#### Inverter Section

The Inverter section of the Converters and DC Bus tab displays the parameters of the Universal Bridge block of the Fundamental Blocks (powerlib) library. For more information on the Universal Bridge parameters, refer to the Universal Bridge reference page.

The average-value inverter uses the following parameter.

On-state resistance

The on-state resistance of the inverter switches (ohms). Default is `1e-3`.

### Controller Tab

Regulation type

This pop-up menu allows you to choose between speed and torque regulation. Default is `Speed regulation`.

Schematic

When you click 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 (rpm/s). An excessively large positive value can cause DC bus under-voltage. This parameter is used in speed regulation mode only. Default is `1000`.

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. Default is `-1000`.

Speed cutoff frequency

The speed measurement first-order low-pass filter cutoff frequency (Hz). This parameter is used in speed regulation mode only. Default is `100`.

Speed controller sampling time

The speed controller sampling time (s). The sampling time must be a multiple of the simulation time step. Default is `7*20e-6`.

PI regulator — Proportional gain

The speed controller proportional gain. This parameter is used in speed regulation mode only. Default is `5`.

PI regulator — Integral gain

The speed controller integral gain. This parameter is used in speed regulation mode only. Default is `100`.

Torque output limits — Negative

The maximum negative demanded torque applied to the motor by the current controller (N.m). Default is `-17.8`.

Torque output limits — Positive

The maximum positive demanded torque applied to the motor by the current controller (N.m). Default is `17.8`.

#### Current Controller Section

Sampling time

The current controller sampling time (s). The sampling time must be a multiple of the simulation time step. Default is `20e-6`.

Current controller hysteresis band

The current hysteresis bandwidth. This value is the total bandwidth distributed symmetrically around the current set point (A). The following figure illustrates a case where the current set point is Is* and the current hysteresis bandwidth is set to dx. Default is `0.01`.

This parameter is not used when using the average-value inverter.

### Note

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

Maximum switching frequency

The maximum inverter switching frequency (Hz). This parameter is not used when using the average-value inverter. Default is `20e3`.

## 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

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 drive parameter set. The specifications of the 3-hp drive are shown in the following table.

3 HP Drive Specifications

Drive Input Voltage

Amplitude

220 V

Frequency

60 Hz

Motor Nominal Values

Power

3 hp

Speed

1650 rpm

Voltage

300 Vdc

## Examples

The `ac7_example` example illustrates an AC7 motor drive simulation with standard load condition.

## References

[1] Bose, B. K. Modern Power Electronics and AC Drives. Upper Saddle River, NJ: Prentice-Hall, 2002.

[2] Krause, P. C. Analysis of Electric Machinery. New York: McGraw-Hill, 1986.

[3] Tremblay, O. Modélisation, simulation et commande de la machine synchrone à aimants à force contre-électromotrice trapézoïdale. Montreal, Canada: École de Technologie Supérieure, 2006.