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

The Field-Oriented Control Induction Motor Drive block represents a standard vector or rotor field-oriented control drive for induction motors. This drive features closed-loop speed control based on the indirect or feedforward vector control method. The speed control loop outputs the reference electromagnetic torque and rotor flux of the machine. The reference direct and quadrature (dq) components of the stator current, corresponding to the commanded rotor flux and torque, are derived based on the indirect vector control strategy. The reference dq components of the stator current are then used to obtain the required gate signals for the inverter through a hysteresis-band or PWM current controller.

The main advantage of this drive compared to scalar-controlled drives is its fast dynamic response. The inherent coupling effect between the torque and flux in the machine is managed through decoupling (rotor flux orientation) control, which allows the torque and flux to be controlled independently. However, due to its computation complexity, the implementation of this drive requires fast computing processors or DSPs.

**Note**

In Simscape™
Electrical™ Specialized Power Systems software, the Field-Oriented Control Induction
Motor Drive block is commonly called the `AC3`

motor drive.

The Field-Oriented Control Induction Motor Drive block uses these blocks from the Electric Drives / Fundamental Drive Blocks library:

Speed Controller (AC)

Field-Oriented Controller

DC Bus

Inverter (Three-Phase)

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 cannot be higher than the FOC time step.

**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 bus 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.**Set sensorless**When you select this check box, the motor speed is estimated from terminal voltages and currents based on the Model Referencing Adaptive System (MRAS) technique. The

**Sensorless**tab contains the estimator controller parameters.When this check box is cleared, the motor speed is measured by an internal speed sensor, and the

**Sensorless**tab is not displayed on the block mask.

The **Asynchronous Machine** tab displays the parameters of the
Asynchronous Machine block of the Fundamental Blocks (powerlib) library.

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.

**Capacitance**The DC bus capacitance (F). Default is

`2000e-6`

.

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

`310`

.

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 parameters.

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

`60`

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

`1e-3`

.

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

`Speed regulation`

.**Modulation type**Select hysteresis or space vector modulation. The default modulation type is

`Hysteresis`

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

**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

`900`

.**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

`-900`

.**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

`1000`

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

`100e-6`

.**PI regulator — Proportional gain**The speed controller proportional gain. This parameter is used in speed regulation mode only. Default is

`300`

.**PI regulator — Integral gain**The speed controller integral gain. This parameter is used in speed regulation mode only. Default is

`2000`

.**Torque output limits — Negative**The maximum negative demanded torque applied to the motor by the current controller (N.m). Default is

`-1200`

.**Torque output limits — Positive**The maximum positive demanded torque applied to the motor by the current controller (N.m). Default is

`1200`

.

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

`100`

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

`30`

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

`-2`

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

`2`

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

`16`

.**Sampling Time**The FOC 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)}. Default is`10`

. 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. Default is

`20000`

.**Show/Hide Autotuning Control**Select to show or hide the parameters of the Autotuning Control tool.

**Desired damping [zeta]**Specify the damping factor used for the calculation of the Kp and Ki gains of the Speed Controller (AC) block. Default is

`0.9`

.**Desired response time @ 5% [Trd (sec)]**Specify the desired settling time of the Speed Controller (AC) block. This is time required for the controller response to reach and stay within a 5 percent range of the target value. Default is

`0.1`

.**Bandwidth ratio (InnerLoop/SpeedLoop)**Specify the ratio between the bandwidth and natural frequency of the regulator. Default is

`30`

.**Calculate PI regulator gains**Compute the

**Proportional gain**and**Integral gain**parameters of the Speed Controller (AC) and of the Field-Oriented Controller blocks. The computation is based on the**Desired damping [zeta]**,**Desired response time @ 5%**, and**Bandwidth ratio (InnerLoop/SpeedLoop)**parameters. The computed values are displayed in the mask of the Drive block. Click**Apply**or**OK**to confirm them.

**Proportional gain**Specify the value of the proportional gain of the PI regulator that is used to tune the motor speed.

Default is

`5000`

.**Integral gain**Specify the value of the integral gain of the PI regulator that is used to tune the motor speed.

Default is

`50`

.**Upper - Upper output limit**Specify the upper output limit of the PI controller.

Default is

`500`

.**Lower - Lower output limit**Specify the lower output limit of the PI controller.

Default is

`-500`

.**Controller sample time**Controller sample time, in s. The sample time must be a multiple of the simulation time step. Default is

`2e-06`

.

`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.

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

[2] Grelet, G., and G. Clerc. *Actionneurs
électriques*. Paris: Éditions Eyrolles, 1997.

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