Although the Electric Drives library contains models of motor drives widely used in the industry, you might have some specific requirements leading you to build your own motor drive model. The following information describes how to build a motor drive model using Simulink^{®} and Simscape™ Power Systems™ blocks. You will build the fieldorientedcontrol motor drive, very similar to the AC3 model of the electric drive library. The following figure shows the block diagram of the drive.
FieldOriented VariableFrequency Induction Motor Drive
The induction motor is fed by a currentcontrolled PWM inverter, which operates as a threephase sinusoidal current source. The motor speed ω is compared to the reference ω* and the error is processed by the speed controller to produce a torque command Te*.
As shown below, the rotor flux and torque can be separately controlled by the stator directaxis current i_{ds} and quadratureaxis current i_{qs}, respectively.
FieldOriented Control Principle
The mathematical principles of this AC drive have been discussed in Electric Drives Library. Here, we will only rewrite the basic equations. The stator quadratureaxis current reference i_{qs}* is calculated from torque reference T_{e}* as
$${i}_{qs}*=\frac{2}{3}\cdot \frac{2}{p}\cdot \frac{{L}_{r}}{{L}_{m}}\cdot \frac{{T}_{e}*}{{\psi}_{r}{}_{est}}$$
where L_{r} is the rotor inductance, L_{m} is the mutual inductance, and ψ_{r}_{est} is the estimated rotor flux linkage given by
$${\psi}_{r}{}_{est}=\frac{{L}_{m}\cdot {i}_{ds}}{1+{\tau}_{r}\cdot s}$$
where τ_{r} = L_{r }/ R_{r} is the rotor time constant.
The stator directaxis current reference i_{ds}* is obtained from rotor flux reference input ψ_{r}*.
$${i}_{ds}*=\frac{\left{\psi}_{r}\right*}{{L}_{m}}$$
The rotor flux position Θ_{e} required for coordinates transformation is generated from the rotor speed ω_{m} and slip frequency ω_{sl}.
$${\theta}_{e}={\displaystyle \int \left({\omega}_{m}+{\omega}_{sl}\right)}dt$$
The slip frequency is calculated from the stator reference current i_{qs}* and the motor parameters.
$${\omega}_{sl}=\frac{{L}_{m}}{{\psi}_{r}{}_{est}}\cdot \frac{{R}_{r}}{{L}_{r}}\cdot {i}_{qs}*$$
The i_{qs}* and i_{ds}* current references are converted into phase current references i_{a}*, i_{b}*, i_{c}* for the current regulators. The regulators process the measured and reference currents to produce the inverter gating signals.
The role of the speed controller is to keep the motor speed equal to the speed reference input in steady state and to provide a good dynamic during transients. The controller can be a proportionalintegral type.
Open the power_acdrive
model
and save it as case3
in your working directory
so that you can make further modifications without altering the original
file.
The next figure shows the power_acdrive
model
in which blocks from Simscape Power Systems and Simulink libraries
are used to model the induction motor drive.
Vector Control of AC Motor Drive (power_acdrive)
The induction motor is modeled by an Asynchronous Machine block. The motor used in this case study is a 50 HP, 460 V, fourpole, 60 Hz motor having the following parameters:
Rs 

Lls 

Lm 

Rr 

Llr 

The reference speed and the load torque applied to the motor shaft can be both selected by a Manual Switch block in order to use either a constant value or a step function. Initially the reference speed is set to a constant value of 120 rad/s and the load torque is also maintained constant at 0 N.m
The fieldoriented control is modeled by the Vector Control block, as shown in Vector Control of AC Motor Drive (power_acdrive). This block consists of Simulink blocks shown in the following figure.
Vector Control Block
The IGBT inverter is modeled by a Universal
Bridge block in which the Power Electronic device and Port
configuration options are selected as IGBT/Diode
and ABC
as
output terminals respectively. The DC link input voltage is represented
by a 780 V DC voltage source.
The current regulator consists of three hysteresis controllers and is built with Simulink blocks. The motor currents are provided by the measurement output of the Asynchronous Machine block.
The conversions between abc and dq reference frames are executed by the abc_to_dq0 Transformation and dq0_to_abc Transformation blocks
abc_dq
dq_abc
The rotor flux is calculated by the Flux_Calculation block.
The rotor flux position (Θe) is calculated by the Teta Calculation in Vector Control Block. The motor speed is provided by the measurement output of the Asynchronous Machine block.
The stator quadratureaxis current reference (iqs*) is calculated by the iqs*_Calculation block.
The stator directaxis current reference (ids*) is calculated by the id*_Calculation block.
The speed controller is of proportionalintegral type and is implemented using Simulink blocks.
In order to increase simulation speed, this model is discretized
using a sample time of 2 µs. The variable Ts = 2e6
automatically
loads into your workspace when you open this model. This sample time
Ts is used both for the power circuit (Ts
specified
in the Powergui) and the control system.
Run the simulation by selecting Simulation > Run.
The motor voltage and current waveforms as well as the motor speed and torque are displayed on four axes of the scope connected to the variables Vab, Iabc, ωm, and Te.
You can start the drive by specifying [1,0,0,0,0,0,0,0]
as
the initial conditions for the Asynchronous
Machine block (initial slip = 1 and no currents flowing in
the three phases). The speed reference is 120 rad/s.
The motor speed, electromechanical torque, and currents observed during the starting of the induction motor drive are shown in Starting the Induction Motor Drive.
Note that you can save the final system state vector xFinal
by
selecting Simulation > Configuration parameters >
Data Import/Export, and then selecting the Final
states check box. It can be used as the initial state in
a subsequent simulation so that the simulation can start under steadystate
conditions.
Starting the Induction Motor Drive
When the steady state is attained, you can stop the simulation and zoom on the scope signals.
This figure shows the motor voltage, current, and torque waveforms obtained when the motor is running at no load (torque = 0 N.m) at a speed of 120 rad/s.
The 20 A band imposed by the hysteresis current regulator is clearly seen on the three motor currents.
SteadyState Motor Current, Voltage, and Torque Waveforms
You can study the drive dynamic performance (speed regulation performance versus reference and load torque changes) by applying two changing operating conditions to the drive: a step change in speed reference and a step change in load torque.
Use the Reference Speed selection switch and the Torque selection
switch to set speed reference steps from 120 rad/s to 160 rad/s at
t = 0.2 s and the load torque steps from 0 N.m to 200 N.m at t = 1.8
s. The final state vector obtained with the previous simulation can
be used as the initial condition so that the simulation starts from
steady state. Load the power_acdrive_init.mat
file,
which creates the xInitial
variable. Select Simulation
> Configuration parameters > Data Import/Export,
then select the Initial state check box under Load
from workspace and click OK, and
then restart the simulation.
The response of the induction motor drive to successive changes in speed reference and load torque is shown here.
Dynamic Performance of the Induction Motor Drive
[1] Leonhard, W., Control of Electrical Drives, SpringerVerlag, Berlin, 1996.
[2] Murphy, J. M. D., and Turnbull, F. G., Power Electronic Control of AC Motors, Pergamon Press, Oxford, 1985.
[3] Bose, B. K., Power Electronics and AC Drives, PrenticeHall, Englewood Cliffs, N.J., 1986.