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Asynchronous Machine :: Blocks (SimPowerSystems™)jar:file:///D:/Program%20Files/MATLAB/R2010a/help/
Asynchronous Machine
Model the dynamics of three-phase asynchronous machine, also known as induction machine
Library
Machines
Description
The Asynchronous Machine block operates in either generator or motor mode. The mode of operation is dictated by the sign of the mechanical
torque:
If Tm is positive, the machine acts as a motor.
If Tm is negative, the machine acts as a generator.
The electrical part of the machine is represented by a fourth-order state-space model and the mechanical part by a second-order system. All
electrical variables and parameters are referred to the stator. This is indicated by the prime signs in the machine equations given below. All stator
and rotor quantities are in the arbitrary two-axis reference frame (dq frame). The subscripts used are defined as follows:
SubscriptDefinition
d
q
r
s
l
m
d axis quantity
q axis quantity
Rotor quantity
Stator quantity
Leakage inductance
Magnetizing inductance
Electrical System
Mechanical System
The Asynchronous Machine block parameters are defined as follows (all quantities are referred to the stator):
sls
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Parameter
R, L
R', L'
L
L, L'
V, i
V', i'
V, i
V', i'
ϕ, ϕ
ϕ', ϕ'
ω
Θ
p
ω
Θ
T
T
J
H
F
Definition
Stator resistance and leakage inductance
Rotor resistance and leakage inductance
Magnetizing inductance
Total stator and rotor inductances
q axis stator voltage and current
q axis rotor voltage and current
d axis stator voltage and current
d axis rotor voltage and current
Stator q and d axis fluxes
Rotor q and d axis fluxes
Angular velocity of the rotor
Rotor angular position
Number of pole pairs
Electrical angular velocity (ω x p)
Electrical rotor angular position (Θ x p)
Electromagnetic torque
Shaft mechanical torque
Combined rotor and load inertia coefficient. Set to infinite to simulate locked rotor.
Combined rotor and load inertia constant. Set to infinite to simulate locked rotor.
Combined rotor and load viscous friction coefficient
Dialog Box and Parameters
You can choose between two Asynchronous Machine blocks to specify the electrical and mechanical parameters of the model, by using the pu
Units dialog box or the SI dialog box. Both blocks are modeling the same asynchronous machine model. Depending on the dialog box you
®
choose to use, SimPowerSystems™ software automatically converts the parameters you enter into per unit parameters. The Simulink model of
the Asynchronous Machine block uses pu parameters.
Configuration Tab
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Asynchronous Machine :: Blocks (SimPowerSystems™)jar:file:///D:/Program%20Files/MATLAB/R2010a/help/
Preset model
Provides a set of predetermined electrical and mechanical parameters for various asynchronous machine ratings of power (HP),
phase-to-phase voltage (V), frequency (Hz), and rated speed (rpm).
Select one of the preset models to load the corresponding electrical and mechanical parameters in the entries of the dialog box. Note that
the preset models do not include predetermined saturation parameters. Select No if you do not want to use a preset model, or if you want to
modify some of the parameters of a preset model, as described below.
When you select a preset model, the electrical and mechanical parameters in the Parameters tab of the dialog box become unmodifiable
(grayed out). To start from a given preset model and then modify machine parameters, you have to do the following:
the desired preset model to initialize the parameters.
the Preset model parameter value to No. This will not change the machine parameters. By doing so, you just break the
connection with the particular preset model.
the machine parameters as you wish, then click Apply.
Mechanical input
Allows you to select either the torque applied to the shaft or the rotor speed as the Simulink signal applied to the block's input.
Select Torque Tm to specify a torque input, in N.m or in pu, and change labeling of the block's input to Tm. The machine speed is
determined by the machine Inertia J (or inertia constant H for the pu machine) and by the difference between the applied mechanical torque
Tm and the internal electromagnetic torque Te. The sign convention for the mechanical torque is the following: when the speed is positive,
a positive torque signal indicates motor mode and a negative signal indicates generator mode.
Select Speed w to specify a speed input, in rad/s or in pu, and change labeling of the block's input to w. The machine speed is imposed
and the mechanical part of the model (Inertia J) is ignored. Using the speed as the mechanical input allows modeling a mechanical
coupling between two machines and interfacing with SimMechanics™ and SimDriveline™ models.
The next figure indicates how to model a stiff shaft interconnection in a motor-generator set when friction torque is ignored in machine 2.
The speed output of machine 1 (motor) is connected to the speed input of machine 2 (generator), while machine 2 electromagnetic torque
output Te is applied to the mechanical torque input Tm of machine 1. The Kw factor takes into account speed units of both machines (pu or
rad/s) and gear box ratio w2/w1. The KT factor takes into account torque units of both machines (pu or N.m) and machine ratings. Also, as
the inertia J2 is ignored in machine 2, J2 referred to machine 1 speed must be added to machine 1 inertia J1.
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Asynchronous Machine :: Blocks (SimPowerSystems™)jar:file:///D:/Program%20Files/MATLAB/R2010a/help/
Rotor type
Specifies the branching for the rotor windings.
Reference frame
Specifies the reference frame that is used to convert input voltages (abc reference frame) to the dq reference frame, and output currents
(dq reference frame) to the abc reference frame. You can choose among the following reference frame transformations:
Rotor (Park transformation)
Stationary (Clarke or αβ transformation)
Synchronous
The following relationships describe the abc-to-dq reference frame transformations applied to the Asynchronous Machine phase-to-phase
voltages.
In the preceding equations, Θ is the angular position of the reference frame, while is the difference between the position of the
reference frame and the position (electrical) of the rotor. Because the machine windings are connected in a three-wire Y configuration,
there is no homopolar (0) component. This also justifies the fact that two line-to-line input voltages are used inside the model instead of
three line-to-neutral voltages. The following relationships describe the dq-to-abc reference frame transformations applied to the
Asynchronous Machine phase currents.
The following table shows the values taken by Θ and β in each reference frame (Θ
e
is the position of the synchronously rotating reference
frame).
Reference FrameΘ
Rotor
Stationary
Synchronous
Θ
r
0
Θ
e
β
0
-Θ
r
Θ
e
- Θ
r
The choice of reference frame affects the waveforms of all dq variables. It also affects the simulation speed and in certain cases the
accuracy of the results. The following guidelines are suggested in [1]:
Use the stationary reference frame if the stator voltages are either unbalanced or discontinuous and the rotor voltages are balanced
(or 0).
Use the rotor reference frame if the rotor voltages are either unbalanced or discontinuous and the stator voltages are balanced.
Use either the stationary or synchronous reference frames if all voltages are balanced and continuous.
Mask units
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Asynchronous Machine :: Blocks (SimPowerSystems™)jar:file:///D:/Program%20Files/MATLAB/R2010a/help/
Specifies the units of the electrical and mechanical parameters of the model. This parameter is not modifiable; it is provided for information
purposes only.
Parameters Tab
Nominal power, voltage (line-line), and frequency
The nominal apparent power Pn (VA), RMS line-to-line voltage Vn (V), and frequency fn (Hz).
Stator resistance and inductance
The stator resistance Rs (Ω or pu) and leakage inductance Lls (H or pu).
Rotor resistance and inductance
The rotor resistance Rr' (Ω or pu) and leakage inductance Llr' (H or pu), both referred to the stator.
Mutual inductance
The magnetizing inductance Lm (H or pu).
Inertia constant, friction factor, and pole pairs
2
For the SI units dialog box: the combined machine and load inertia coefficient J (kg.m), combined viscous friction coefficient F (N.m.s),
and pole pairs p. The friction torque Tf is proportional to the rotor speed ω (Tf = F.w).
For the pu units dialog box: the inertia constant H (s), combined viscous friction coefficient F (pu), and pole pairs p.
Initial conditions
Specifies the initial slip s, electrical angle Θe (degrees), stator current magnitude (A or pu), and phase angles (degrees):
[slip, th, i
as
, i
bs
, i
cs
, phase
as
, phase
bs
, phase
cs
]
For the wound-rotor machine, you can also specify optional initial values for the rotor current magnitude (A or pu), and phase angles
(degrees):
[slip, th, i
as
, i
bs
, i
cs
, phase
as
, phase
bs
, phase
cs
, i
ar
, i
br
, i
cr
,
phase
ar
, phase
br
, phase
cr
]
For the squirrel cage machine, the initial conditions can be computed by the load flow utility in the Powergui block.
Simulate saturation
Specifies whether magnetic saturation of rotor and stator iron is simulated or not.
Saturation parameters
Specifies the no-load saturation curve parameters. Magnetic saturation of stator and rotor iron (saturation of the mutual flux) is modeled by
a nonlinear function (in this case a polynomial) using points of the no-load saturation curve. You must enter a 2-by-n matrix, where n is the
number of points taken from the saturation curve. The first row of this matrix contains the values of stator currents, while the second row
contains values of corresponding terminal voltages (stator voltages). The first point (first column of the matrix) must correspond to the point
where the effect of saturation begins.
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You must select the Simulate saturation check box to simulate saturation. If the Simulate saturation is not selected, the relationship
between the stator current and the stator voltage is linear.
Advanced Tab
Sample time (-1 for inherited)
Specifies the sample time used by the block. To inherit the sample time specified in the Powergui block, set this parameter to -1.
Inputs and Outputs
Tm
The Simulink input of the block is the mechanical torque at the machine's shaft. When the input is a positive Simulink signal, the
asynchronous machine behaves as a motor. When the input is a negative signal, the asynchronous machine behaves as a generator.
When you use the SI parameters mask, the input is a signal in N.m, otherwise it is in pu.
w
The alternative block input (depending on the value of the
Mechanical input
parameter) is the machine speed, in rad/s.
m
The Simulink output of the block is a vector containing 21 signals. You can demultiplex these signals by using the Bus Selector block
provided in the Simulink library. Depending on the type of mask you use, the units are in SI, or in pu.
SignalDefinition
1
2
3
4
5
6
7
8
Rotor current ir_a
Rotor current ir_b
Rotor current ir_c
Rotor current iq
Rotor current id
Rotor flux phir_q
Rotor flux phir_d
Rotor voltage Vr_q
Units
A or pu
A or pu
A or pu
A or pu
A or pu
V.s or pu
V.s or pu
V or pu
Symbol
i'
ra
i'
rb
i'
rc
i'
qr
i'
dr
ϕ'
qr
ϕ'
dr
v'
qr
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SignalDefinition
9
10
11
12
13
14
15
16
17
18
19
20
21
Rotor voltage Vr_d
Stator current is_a
Stator current is_b
Stator current is_c
Stator current is_q
Stator current is_d
Stator flux phis_q
Stator flux phis_d
Stator voltage vs_q
Stator voltage vs_d
Rotor speed
Electromagnetic torque Te
Rotor angle thetam
Units
V or pu
A or pu
A or pu
A or pu
A or pu
A or pu
V.s or pu
V.s or pu
V or pu
V or pu
rad/s
N.m or pu
rad
Symbol
v'
d
i
sa
i
sb
i
sc
i
qs
i
ds
ϕ
qs
ϕ
ds
v
qs
v
ds
ω
m
T
e
Θ
m
The stator terminals of the Asynchronous Machine block are identified by the A, B, and C letters. The rotor terminals are identified by the a, b,
and c letters. Note that the neutral connections of the stator and rotor windings are not available; three-wire Y connections are assumed.
Limitations
Asynchronous Machine block does not include a representation of the saturation of leakage fluxes. You must be careful when you
connect ideal sources to the machine's stator. If you choose to supply the stator via a three-phase Y-connected infinite voltage source, you
must use three sources connected in Y. However, if you choose to simulate a delta source connection, you must use only two sources
connected in series.
2.
When you use Asynchronous Machine blocks in discrete systems, you might have to use a small parasitic resistive load, connected at the
machine terminals, in order to avoid numerical oscillations. Large sample times require larger loads. The minimum resistive load is
proportional to the sample time. As a rule of thumb, remember that with a 25 μs time step on a 60 Hz system, the minimum load is
approximately 2.5% of the machine nominal power. For example, a 200 MVA asynchronous machine in a power system discretized with a
50 μs sample time requires approximately 5% of resistive load or 10 MW. If the sample time is reduced to 20 μs, a resistive load of 4 MW
should be sufficient.
Examples
Example 1: Use of the Asynchronous Machine Block in Motor Mode
The power_pwm demo illustrates the use of the Asynchronous Machine block in motor mode. It consists of an asynchronous machine in an
open-loop speed control system.
The machine's rotor is short-circuited, and the stator is fed by a PWM inverter, built with Simulink blocks and interfaced to the Asynchronous
Machine block through the Controlled Voltage Source block. The inverter uses sinusoidal pulse-width modulation, which is described in [2]. The
base frequency of the sinusoidal reference wave is set at 60 Hz and the triangular carrier wave's frequency is set at 1980 Hz. This corresponds
to a frequency modulation factor m
f
of 33 (60 Hz x 33 = 1980). It is recommended in [2] that m
f
be an odd multiple of three and that the value be
as high as possible.
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The 3 HP machine is connected to a constant load of nominal value (11.9 N.m). It is started and reaches the set point speed of 1.0 pu at t = 0.9
second.
The parameters of the machine are those found in the SI Units dialog box above, except for the stator leakage inductance, which is set to twice
its normal value. This is done to simulate a smoothing inductor placed between the inverter and the machine. Also, the stationary reference
frame was used to obtain the results shown.
Open the power_pwm demo. Note in the simulation parameters that a small relative tolerance is required because of the high switching rate of
the inverter.
Run the simulation and observe the machine's speed and torque.
The first graph shows the machine's speed going from 0 to 1725 rpm (1.0 pu). The second graph shows the electromagnetic torque developed
by the machine. Because the stator is fed by a PWM inverter, a noisy torque is observed.
However, this noise is not visible in the speed because it is filtered out by the machine's inertia, but it can also be seen in the stator and rotor
currents, which are observed next.
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Finally, look at the output of the PWM inverter. Because nothing of interest can be seen at the simulation time scale, the graph concentrates on
the last moments of the simulation.
Example 2: Effect of Saturation of the Asynchronous Machine Block
The power_asm_sat demo illustrates the effect of saturation of the Asynchronous Machine block.
Two identical three-phase motors (50 HP, 460 V, 1800 rpm) are simulated with and without saturation, to observe the saturation effects on the
stator currents. Two different simulations are realized in the demo.
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The first simulation, is the no-load steady-state test. The table below contains the values of the Saturation Parameters and the measurements
obtained by simulating different operating points on the saturated motor (no-load and in steady-state).
Saturation Parameters
Vsat (Vrms L-L)
-
230
-
-
322
-
-
414
-
-
460
-
-
506
-
Isat (peak A)
-
14.04
-
-
27.81
-
-
53.79
-
-
72.69
-
-
97.98
-
Measurements
Vrms L-LIs_A (peak A)
120
230
250
300
322
351
382
414
426
449
460
472
488
506
519
7.322
14.03
16.86
24.04
28.39
35.22
43.83
54.21
58.58
67.94
73.01
79.12
88.43
100.9
111.6
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Saturation Parameters
Vsat (Vrms L-L)
-
-
552
-
-
598
-
-
644
-
-
-
690
Isat (peak A)
-
-
148.68
-
-
215.74
-
-
302.98
-
-
-
428.78
Measurements
Vrms L-LIs_A (peak A)
535
546
552
569
581
598
620
633
644
659
672
681
690
126.9
139.1
146.3
169.1
187.4
216.5
259.6
287.8
313.2
350
383.7
407.9
432.9
The graph below illustrates these results and shows the accuracy of the saturation model. As you can see, the measured operating points fit well
the curve that is plotted from the Saturation Parameters data.
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Asynchronous Machine :: Blocks (SimPowerSystems™)jar:file:///D:/Program%20Files/MATLAB/R2010a/help/
Running the simulation with a blocked rotor or with many different values of load torque will allow the observation of other effects of saturation on
the stator currents.
References
[1] Krause, P.C., O. Wasynczuk, and S.D. Sudhoff, Analysis of Electric Machinery, IEEE Press, 2002.
[2] Mohan, N., T.M. Undeland, and W.P. Robbins, Power Electronics: Converters, Applications, and Design, John Wiley & Sons, Inc., New York,
1995, Section8.4.1.
See Also
Powergui
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