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Implement field-oriented control (FOC) induction motor drive model

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 from blocks provided in the SimPowerSystems™ library. The speed controller, the braking chopper, and the FOC models are from blocks provided in the Electric Drives library. It is possible to use a simplified version of the drive containing an average-value model of the inverter and allowing faster simulation.

The speed controller is based on a PI regulator, shown below. The outputs of this regulator are set points for the torque and the flux applied to the FOC block.

The FOC block contains eleven main blocks. These blocks are
described below in the Indirect Vector Control Simulink^{®} Schematic.

The ψ_{r}* calculation* block
is used to estimate the motor's rotor flux. This calculation is based
on motor equation synthesis.

The Θ_{e}_{ }*calculation* block
is used to find the phase angle of the rotor flux rotating field.

The *abc-dq** *block* *performs the conversion of *abc* phase
variables into *dq* components of the rotor flux
rotating field reference frame.

The *dq-abc** *block* *performs the conversion of the *dq* component
of the rotor flux rotating field reference frame into *abc* phase
variables.

The *iqs*calculation* block uses the calculated
rotor flux and the torque reference to compute the stator current
quadrature component required to produce the electromagnetic torque
on the motor's shaft.

The* ids*calculation* block uses the rotor
flux reference to compute the stator current direct component required
to produce the rotor flux in the machine.

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

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

The *flux controller* is used to control
the flux dynamics and to reduce the steady-state flux error.

The *magnetization vector* unit contains
the vector used to create the motor initial flux.

The *magnetization control* unit contains
the logic used to switch between the magnetization and normal operation
mode.

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 current sources and two 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:

*I*_{dc} = (*P*_{out} + *P*_{losses})
/ *V*_{in},

with *P*_{out} being the
output power and *P*_{losses} the
losses in the power electronics devices and *V*_{in} the
DC bus voltage.

On the AC side, the current sources represent the average phase currents fed to the motor. The regulation being fast, the current values are set equal to the current references sent by the current regulator. A small current is injected to compensate the current drawn by the three-phase load (needed because of the inverter current sources in series with inductive motor).

During loss of current tracking due to insufficient inverter voltage, the currents are fed by two controlled voltage sources. These voltage sources represent the square wave mode and allow good representation of the phase currents during inverter saturation. Each voltage source outputs either Vin or 0, depending on the values of the pulses (1 or 0) sent by the current controller.

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

FOC sampling time

The speed controller sampling time has to be a multiple of the FOC 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 an FOC sampling time of 60 µs, good simulation results have been obtained for a simulation time step of 60 µs. This time step can, of course, not be higher than the FOC time step.

The **Asynchronous Machine** tab
displays the parameters of the Asynchronous 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.

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.

The **Inverter** 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.

The average-value inverter uses the following parameters.

**Source frequency**The frequency of the three-phase voltage source (Hz).

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

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 (V). 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 (V). The Chopper hysteresis logic is shown in the next 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).

**Flux Controller — Proportional gain**The flux controller proportional gain.

**Flux Controller — Integral gain**The flux controller integral gain.

**Flux output limits — Positive**The flux controller maximum positive output (Wb).

**Flux output limits — Negative**The flux controller maximum negative output (Wb).

**Lowpass filter cutoff frequency**The flux estimation first-order filter cutoff frequency (Hz).

**Sampling Time**The FOC 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.

**Maximum Switching Frequency**The maximum inverter switching frequency (Hz). 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

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.

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 | 460 V | |

Frequency | 60 Hz | 60 Hz | |

| |||

Power | 3 hp | 200 hp | |

Speed | 1705 rpm | 1785 rpm | |

Voltage | 220 V | 460 V |

The `ac3_example` example illustrates
an AC3 motor drive simulation with standard load conditions for the
detailed and average-value models.

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. Notice that the results of the average-value model are similar to those of the detailed model except that the higher frequency signal components are not represented with the average-value converter.

**AC3 Example Waveforms (Blue : Detailed Converter,
Red : Average-Value Converter)**

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