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

The high-level schematic shown below is built from six main blocks. The PMSM, the three-phase inverter, and the three-phase diode rectifier models are provided with the SimPowerSystems™ library. The speed controller, the braking chopper, and the current controller models are specific to the Electric Drives library. It is possible to use a simplified version of the drive containing an average-value model of the inverter for faster simulation.

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

The current controller contains four main blocks, shown below. These blocks are described below.

The *T-I* block performs the conversion from
the reference torque to the peak reference current. The relation used
to convert torque to current assumes pure rectangular current waveforms.
In practice, due to the motor inductance, it's impossible to obtain
these currents. Therefore the electromagnetic torque may be lower
than the reference torque, especially at high speed.

The *Hall decoder* block is used to extract
the BEMF information from the Hall effect signals. The outputs, three-level
signals (−1, 0, 1), represent the normalized ideal phase currents
to be injected in the motor phases. These type of currents will produce
a constant torque. The following figure shows the BEMF of phase A
and the output of the Hall decoder for the phase A.

The *current regulator* is a bang-bang current
controller with adjustable hysteresis bandwidth.

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

When using the average-value inverter, the *abc* current
references are sent to the simplified inverter.

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.

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

It is composed of one controlled current source on the DC side and of two controlled voltage sources on the AC side. The DC current source allows the representation of the DC bus current behavior described by the following equation:

*I _{dc}* = (

with *P*_{out} being the
output AC power, *P*_{losses} the
losses in the power electronic devices, and *V*_{in} 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
PMSM documentation for machine model). This dynamic model takes the
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 be applied to
the machine.

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

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

The model is discrete. Good simulation results have been obtained
with a 2 *µ*s 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 *µ*s,
good simulation results have been obtained for a simulation time step
of 40 *µ*s. The simulation time step can, of
course, not be higher than the current controller time step.

The **Permanent
Magnet Synchronous Machine** tab displays the parameters
of the Permanent Magnet Synchronous Machine block of
the 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:

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.

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

The average-value inverter uses the following parameter.

**On-state resistance**The on-state resistance of the inverter switches (ohms).

**DC Bus Field — 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 (ohms).

**Frequency**The braking chopper frequency (Hz).

**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.

**Deactivation 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 in the following figure.

**Regulation Type**This pop-up menu allows you to choose between speed and torque regulation.

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

**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).

**Sampling Time**The current controller sampling time (s). The sampling time must be a multiple of the simulation time step.

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

`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.

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 | |

| ||

Power | 3 hp | |

Speed | 1650 rpm | |

Voltage | 300 Vdc |

The `ac7_example` example illustrates
an AC7 motor drive simulation with standard load condition. At time
t = 0 s, the speed set point is 300 rpm.

There are two design tools in this example. The first block calculates the gains of the speed regulator in accordance with your specifications. The second block plots the operating regions of the drive. Open these blocks for more information.

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 11 N.m to −11 N.m. The next figure shows the results for the detailed converter and for the average-value converter. Observe that the average voltage, current, torque, and speed values are identical for both models. Notice that the higher frequency signal components are not represented with the average-value converter.

**AC7 Example Waveforms (Blue: Detailed Converter,
Red: Average-Value Converter)**

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

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

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

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