Asynchronous Machine

Model dynamics of three-phase asynchronous machine, also known as induction machine, in SI or pu units

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Libraries:
Simscape / Electrical / Specialized Power Systems / Electrical Machines

Description

The Asynchronous Machine SI Units and Asynchronous Machine pu Units blocks implement a three-phase asynchronous machine (wound rotor, squirrel cage, or double squirrel cage) modeled in a selectable dq reference frame (rotor, stator, or synchronous). Stator and rotor windings are connected in wye to an internal neutral point. The 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 (or sixth-order for the double squirrel-cage machine) state-space model, and the mechanical part by a second-order system. All electrical variables and parameters are referred to the stator, which is indicated by the prime signs in the following machine equations. All stator and rotor quantities are in the arbitrary two-axis reference frame (dq frame). The subscripts used are defined in this table.

Subscript	Definition
d	d-axis quantity
q	q-axis quantity
r	Rotor quantity (wound-rotor or single-cage)
r1	Cage 1 rotor quantity (double-cage)
r2	Cage 2 rotor quantity (double-cage)
s	Stator quantity
l	Leakage inductance
m	Magnetizing inductance

Electrical System of the Wound-Rotor or Squirrel-Cage Machine

V_qs = R_si_qs + dφ_qs/dt + ωφ_ds

V_ds = R_si_ds + dφ_ds/dt – ωφ_qs

V'_qr = R'_ri'_qr + dφ'_qr/dt + (ω – ω_r)φ'_dr

V'_dr = R'_ri'_dr + dφ'_dr/dt – (ω – ω_r)φ'_qr

T_e = 1.5p(φ_dsi_qs – φ_qsi_ds)

ω — Reference frame angular velocity

ω_r — Electrical angular velocity

φ_qs = L_si_qs + L_mi'_qr

φ_ds = L_si_ds + L_mi'_dr

φ'_qr = L'_ri'_qr + L_mi_qs

φ'_dr = L'_ri'_dr + L_mi_ds

L_s = L_ls + L_m

L'_r = L'_lr + L_m

Electrical System of the Double Squirrel-Cage Machine

V_qs = R_si_qs + dφ_qs/dt + ωφ_ds

V_ds = R_si_ds + dφ_ds/dt – ωφ_qs

0 = R'_r1i'_qr1 + dφ'_qr1/dt + (ω – ω_r)φ'_dr1

0 = R'_r1i'_dr1 + dφ'_dr1/dt – (ω – ω_r)φ'_qr1

0 = R'_r2i'_qr2 + dφ'_qr2/dt + (ω – ω_r)φ'_dr2

0 = R'_r2i'_dr2 + dφ'_dr2/dt – (ω – ω_r)φ'_qr2

T_e = 1.5p(φ_dsi_qs – φ_qsi_ds)

φ_qs = L_si_qs + L_m(i'_qr1 + i'_qr2)

φ_ds = L_si_ds + L_m(i'_dr1 + i'_dr2)

φ'_qr1 = L'_r1i'_qr1 + L_mi_qs

φ'_dr1 = L'_r1i'_dr1 + L_mi_ds

φ'_qr2 = L'_r2i'_qr2 + L_mi_qs

φ'_dr2 = L'_r2i'_dr2 + L_mi_ds

L_s = L_ls + L_m

L'_r1 = L'_lr1 + L_m

L'_r2 = L'_lr2 + L_m

Mechanical System

$$\begin{array}{c}\frac{d}{dt}{\omega }_m=\frac{1}{2H}\left(T_e-F{\omega }_m-T_m\right)\\ \frac{d}{dt}{\theta }_m={\omega }_m\end{array}$$

The Asynchronous Machine block parameters are defined in the table. All quantities are referred to the stator.

Parameters Common to All Models	Definition
Rs, Lls	Stator resistance and leakage inductance
Lm	Magnetizing inductance
Ls	Total stator inductance
Vqs, iqs	q-axis stator voltage and current
Vds, ids	d-axis stator voltage and current
ϕqs, ϕϕds	Stator q-axis and d-axis fluxes
ωm	Angular velocity of the rotor
Θm	Rotor angular position
p	Number of pole pairs
ωr	Electrical angular velocity (ωm × p)
Θr	Electrical rotor angular position (Θm × p)
Te	Electromagnetic torque
Tm	Shaft mechanical torque
J	Combined rotor and load inertia coefficient. Set to infinite to simulate locked rotor.
H	Combined rotor and load inertia constant. Set to infinite to simulate locked rotor.
F	Combined rotor and load viscous friction coefficient

Parameters Specific to Single-Cage or Wound Rotor	Definition
L'r	Total rotor inductance
R'r, L'lr	Rotor resistance and leakage inductance
V'qr, i'qr	q-axis rotor voltage and current
V'dr, i'dr	d-axis rotor voltage and current
ϕ'qr, ϕ'dr	Rotor q-axis and d axis fluxes

Parameters Specific to Double-Cage Rotor	Definition
R'r1, L'lr1	Rotor resistance and leakage inductance of cage 1
R'r2, L'lr2	Rotor resistance and leakage inductance of cage 2
L'r1, L'r2	Total rotor inductances of cage 1 and 2
i'qr1, i'qr2	q-axis rotor current of cage 1 and 2
i'dr1, i'dr2	d-axis rotor current of cage 1 and 2
ϕ'qr1, ϕ'dr1	q-axis and d-axis rotor fluxes of cage 1
ϕ'qr2, ϕ'dr2	q-axis and d-axis rotor fluxes of cage 2

Assumptions and Limitations

• The Asynchronous Machine blocks do not include a representation of the saturation of leakage fluxes. Be careful when you connect ideal sources to the stator of the machine. 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.

  

• When you use Asynchronous Machine blocks in discrete systems, you might have to connect a small parasitic resistive load at the machine terminals to avoid numerical oscillations. Large sample times require larger loads. The optimum resistive load is proportional to the sample time. 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 is sufficient.

Ports

The stator terminals of the Asynchronous Machine blocks are identified by the letters A, B, and C. The rotor terminals are identified by the letters a, b, and c. The neutral connections of the stator and rotor windings are not available. Three-wire Y connections are assumed.

Input

Tm — Mechanical torque

scalar

Mechanical torque at the machine's shaft, specified as a scalar. When the input is positive, the asynchronous machine behaves as a motor. When the input is negative, the asynchronous machine behaves as a generator.

When you use the Asynchronous Machine SI Units block, the input is a signal in N.m. When you use the Asynchronous Machine pu Units block, the input is a signal in pu.

Dependencies

To enable this port, in the Configuration tab, set the Mechanical input parameter to Torque Tm.

w — Machine speed

scalar

Machine speed in rad/s (for the Asynchronous Machine SI Units block) or in pu (for the Asynchronous Machine pu Units block), specified as a scalar.

Dependencies

To enable this port, in the Configuration tab, set the Mechanical input parameter to Speed w.

Output

m — Measurement signal

28-element vector

Measurement signals, returned as a vector. You can demultiplex these signals by using the Bus Selector block. The units are in SI or pu, depending on whether you use the Asynchronous Machine SI Units or Asynchronous Machine pu Units block. The cage 2 rotor signals return a null signal when the Rotor type parameter on the Configuration tab is set to Wound or Squirrel-cage.

Name	Definition	Units
iar	Rotor current ir_a	A or pu
ibr	Rotor current ir_b	A or pu
icr	Rotor current ir_c	A or pu
iqr	Rotor current iq	A or pu
idr	Rotor current id	A or pu
phiqr	Rotor flux phir_q	V.s or pu
phidr	Rotor flux phir_d	V.s or pu
vqr	Rotor voltage Vr_q	V or pu
vdr	Rotor voltage Vr_d	V or pu
iar2	Cage 2 rotor current ir_a	A or pu
ibr2	Cage 2 rotor current ir_b	A or pu
icr2	Cage 2 rotor current ir_c	A or pu
iqr2	Cage 2 rotor current iq	A or pu
idr2	Cage 2 rotor current id	A or pu
phiqr2	Cage 2 rotor flux phir_q	V.s or pu
phidr2	Cage 2 rotor flux phir_d	V.s or pu
ias	Stator current is_a	A or pu
ibs	Stator current is_b	A or pu
ics	Stator current is_c	A or pu
iqs	Stator current is_q	A or pu
ids	Stator current is_d	A or pu
phiqs	Stator flux phis_q	V.s or pu
phids	Stator flux phis_d	V.s or pu
vqs	Stator voltage vs_q	V or pu
vds	Stator voltage vs_d	V or pu
w	Rotor speed	rad/s
Te	Electromagnetic torque Te	N.m or pu
theta	Rotor angle thetam	rad

Conserving

A — Phase A stator terminal

specialized electrical

Specialized electrical conserving port associated with the phase A stator terminal.

B — Phase B stator terminal

specialized electrical

Specialized electrical conserving port associated with the phase B stator terminal.

C — Phase C stator terminal

specialized electrical

Specialized electrical conserving port associated with the phase C stator terminal.

a — Phase a rotor terminal

specialized electrical

Specialized electrical conserving port associated with the phase a rotor terminal.

Dependencies

This port applies only to the Asynchronous Machine SI Units block.

b — Phase b rotor terminal

specialized electrical

Specialized electrical conserving port associated with the phase b rotor terminal.

Dependencies

This port applies only to the Asynchronous Machine SI Units block.

c — Phase c rotor terminal

specialized electrical

Specialized electrical conserving port associated with the phase c rotor terminal.

Dependencies

This port applies only to the Asynchronous Machine SI Units block.

S — Machine rotor shaft

mechanical

Mechanical rotational conserving port associated with the machine rotor.

Dependencies

To enable this port, in the Configuration tab, set the Mechanical input parameter to Mechanical rotational port.

Parameters

Configuration

Rotor type — Rotor type

Wound | Squirrel-cage | Double squirrel-cage

Type of rotor. For the Asynchronous Machine SI Units block, the default value is Wound. For the Asynchronous Machine pu Units block, the default value is Squirrel-cage.

Squirrel-cage preset model — Electrical and mechanical parameters

No (default) | 01: 5 HP 460 V 60Hz 1750 RPM | 02: 10 HP 460 V 60Hz 1760 RPM | ...

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) for single squirrel-cage machines.

Select one of the preset models to load the corresponding electrical and mechanical parameters. The preset models do not include predetermined saturation parameters. Choices are:

• 01: 5 HP 460 V 60Hz 1750 RPM

• 02: 10 HP 460 V 60Hz 1760 RPM

• 03: 20 HP 460 V 60Hz 1760 RPM

• 04: 50 HP 460 V 60Hz 1780 RPM

• 05: 100 HP 460 V 60Hz 1780 RPM

• 06: 150 HP 460 V 60Hz 1785 RPM

• 07: 200 HP 460 V 60Hz 1785 RPM

• 08: 5 HP 575 V 60Hz 1750 RPM

• 09: 10 HP 575 V 60Hz 1760 RPM

• 10: 20 HP 575 V 60Hz 1765 RPM

• 11: 50 HP 575 V 60Hz 1775 RPM

• 12: 100 HP 575 V 60Hz 1780 RPM

• 13: 150 HP 575 V 60Hz 1785 RPM

• 14: 200 HP 575 V 60Hz 1785 RPM

• 15: 5.4 HP (4KW) 400 V 50Hz 1430 RPM

• 16: 10 HP (7.5KW) 400 V 50Hz 1440 RPM

• 17: 20 HP (15KW) 400 V 50Hz 1460 RPM

• 18: 50 HP (37KW) 400 V 50Hz 1480 RPM

• 19: 100 HP (75KW) 400 V 50Hz 1484 RPM

• 20: 150 HP (110KW) 400 V 50Hz 1487 RPM

• 21: 215 HP (160KW) 400 V 50Hz 1487 RPM

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.

When you select a preset model, the electrical and mechanical parameters in the Parameters tab are dimmed. To start from a preset model and then modify machine parameters:

1. Select the preset model for which you want to initialize the parameters.

2. Change the Preset model parameter to No. This action does not change the machine parameters, but breaks the connection with the preset model.

3. Modify the machine parameters as you want.

Dependencies

To enable this parameter, set Rotor type to Squirrel-cage.

Double squirrel-cage preset model — Preset models

button

Click Open parameter estimator to open an interface to the power_AsynchronousMachineParams function that gives you access to preset models for double-cage asynchronous machines.

Mechanical input — Mechanical input

Torque Tm (default) | Speed w | Mechanical rotational port

Whether to represent the torque applied to the shaft or the rotor speed as a Simulink^® input of the block, or to represent the machine shaft by a Simscape™ rotational mechanical port.

Select Torque Tm to specify a torque input, in N.m or in pu, and and expose the Tm port. The machine speed is determined by the machine inertia J (for the SI machine) or inertia constant H (for the pu machine) and by the difference between the applied mechanical torque Tm, and the internal electromagnetic torque, Te. 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 expose the w port. The machine speed is imposed and the mechanical part of the model (the machine inertia J) is ignored. Using the speed as the mechanical input allows you to model a mechanical coupling between two machines.

The 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 (the motor) is connected to the speed input of machine 2 (the 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 the speed units of both machines (rad/s or pu) and gear box ratio w2/w1. The KT factor takes into account the torque units of both machines (N.m or pu) and machine ratings. Also, because inertia J2 is ignored in machine 2, J2 refers to the speed of machine 1 and must be added to machine 1 inertia J1.

Select Mechanical rotational port to expose a Simscape mechanical rotational port, S, that allows you to connect the machine shaft to other Simscape blocks that have mechanical rotational ports.

The figure indicates how to connect an Ideal Torque Source block from the Simscape library to the machine shaft to represent the machine in motor mode or in generator mode when the rotor speed is positive.

Reference frame — Reference frame for converting

Rotor (default) | Stationary | Synchronous

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. Choose from 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.

$$\begin{array}{c}\left[\begin{array}{c}{V}_{qs}\\ V_{ds}\end{array}\right]=\frac{1}{3}\left[\begin{array}{cc}2\cos \theta & \cos \theta +\sqrt{3}\sin \theta \\ 2\sin \theta & \sin \theta -\sqrt{3}\cos \theta \end{array}\right]\left[\begin{array}{c}{V}_{abs}\\ V_{bcs}\end{array}\right]\\ \left[\begin{array}{c}V{\text{'}}_{qr}\\ V{\text{'}}_{dr}\end{array}\right]=\frac{1}{3}\left[\begin{array}{cc}2\cos \beta & \cos \beta +\sqrt{3}\sin \beta \\ 2\sin \beta & \sin \beta -\sqrt{3}\cos \beta \end{array}\right]\left[\begin{array}{c}V{\text{'}}_{abr}\\ V{\text{'}}_{bcr}\end{array}\right]\end{array}$$

In the preceding equations, Θ is the angular position of the reference frame, while β = θ – θ_r 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 configuration also justifies 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.

$$\begin{array}{c}\left[\begin{array}{c}{i}_{as}\\ i_{bs}\end{array}\right]=\left[\begin{array}{cc}\cos \theta & \sin \theta \\ \frac{-\cos \theta +\sqrt{3}\sin \theta }{2}& \frac{-\sqrt{3}\cos \theta -\sin \theta }{2}\end{array}\right]\left[\begin{array}{c}{i}_{qs}\\ i_{ds}\end{array}\right]\\ \left[\begin{array}{c}i{\text{'}}_{ar}\\ i{\text{'}}_{br}\end{array}\right]=\left[\begin{array}{cc}\cos \beta & \sin \beta \\ \frac{-\cos \beta +\sqrt{3}\sin \beta }{2}& \frac{-\sqrt{3}\cos \beta -\sin \beta }{2}\end{array}\right]\left[\begin{array}{c}i{\text{'}}_{qr}\\ i{\text{'}}_{dr}\end{array}\right]\\ i_{cs}=-i_{as}-i_{bs}\\ i{\text{'}}_{cr}=-i{\text{'}}_{ar}-i{\text{'}}_{br}\end{array}$$

The 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 Frame	Θ	β
Rotor	Θr	0
Stationary	0	−Θr
Synchronous	Θe	Θe − Θr

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.

In the following situations, the Reference frame parameter is not editable and is set internally:

powergui Block Setting	Asynchronous Machine Block Setting	Reference frame Parameter
Simulation type is set to Phasor or Discrete Phasor	—	Synchronous
Simulation type is set to Discrete and the Automatically handle Discrete solver and Advanced tab solver settings of blocks parameter is selected	—	Rotor
Simulation type is set to Discrete	Discrete solver model is set to Trapezoidal robust or Backward Euler robust	Rotor

Dependencies

To enable this parameter, in the powergui block, set Simulation type to Continuous or Discrete and clear Automatically handle Discrete solver and Advanced tab solver settings of blocks. Additionally, on the Advanced tab, set Discrete solver model to Trapezoidal non iterative or Trapezoidal iterative (alg. loop).

Use signal names to identify bus labels — How to identify bus labels

off (default) | on

When this check box is selected, the measurement output uses 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, the measurement output uses the signal definition to identify the bus labels. The labels contain nonalphanumeric characters that are incompatible with some Simulink applications.

Parameters for Asynchronous Machine SI Units Block

Tip

This tab contains the electrical parameters of the machine. To estimate the electrical parameters of a double-cage asynchronous machine based on standard manufacturer specifications, use the power_AsynchronousMachineParams function.

Nominal power, voltage (line-line), and frequency [ Pn(VA),Vn(Vrms),fn(Hz) ] — Nominal power, voltage, and frequency

[1.845e+04 400 50] (default) | three-element vector

Nominal apparent power Pn (VA), RMS line-to-line voltage Vn (V), and frequency fn (Hz).

Vrotor/Vstator voltage ratio — Voltage ratio

1 (default) | positive scalar

Vrotor/Vstator voltage ratio of the wound-rotor asynchronous machine when the rotor is at standstill. Specifying this parameter allows you to get the desired rotor voltage without connecting a transformer at the rotor terminals.

Dependencies

To enable this parameter, in the Configuration tab, set Rotor type to Wound.

Stator resistance and inductance[ Rs(ohm) Lls(H) ] — Stator resistance and leakage inductance

[0.5968 0.0003495] (default) | two-element vector

Stator resistance Rs (Ω) and leakage inductance Lls (H).

Rotor resistance and inductance [ Rr'(ohm) Llr'(H) ] — Rotor resistance and leakage inductance

[0.6258 0.005473] (default) | two-element vector

Rotor resistance Rr' (Ω) and leakage inductance Llr' (H), both referred to the stator.

Dependencies

To enable this parameter, in the Configuration tab, set Rotor type to Wound or Squirrel-cage.

Cage 1 resistance and inductance [ Rr1' (ohm) Llr1' (H) ] — Rotor resistance and leakage inductance

[0.4155 0.002066] (default) | two-element vector

Rotor resistance Rr1' (Ω) and leakage inductance Llr1' (H), both referred to the stator.

Dependencies

To enable this parameter, in the Configuration tab, set Rotor type to Double squirrel-cage.

Cage 2 resistance and inductance [ Rr2' (ohm) Llr2' (H) ] — Rotor resistance and leakage inductance

[0.4168 0.0003495] (default) | two-element vector

Rotor resistance Rr2' (Ω) and leakage inductance Llr2' (H), both referred to the stator.

Dependencies

To enable this parameter, in the Configuration tab, set Rotor type to Double squirrel-cage.

Mutual inductance Lm (H) — Magnetizing inductance

0.0354 (default) | scalar

Magnetizing inductance Lm (H).

Inertia, friction factor, pole pairs [ J(kg.m^2) F(N.m.s) p() ] — Inertia, friction factor, pole pairs

[0.05 0.005879 2] (default) | three-element vector

Combined machine and load inertia coefficient J (kg.m²), 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.ω). Tf is expressed in N.m, F in N.m.s, and ω in rad/s.

Initial conditions — Initial slip s, electrical angle, stator current magnitude, phase angles, rotor current magnitude, and phase angles

[0 0 0 0 0 0 0 0] (default) | eight-element vector

Initial slip s, electrical angle Θe (degrees), stator current magnitude (A), and phase angles (degrees):

[slip, th, ias, ibs, ics, phaseas, phasebs, phasecs]

If the Rotor type parameter (in the Configuration tab) is set to Wound, you can also specify optional initial values for the rotor current magnitude (A), and phase angles (degrees):

[slip, th, ias, ibs, ics, phaseas, phasebs, phasecs, iar, ibr, icr, phasear, phasebr, phasecr]

When the Rotor type parameter (in the Configuration tab) is set to Squirrel-cage, the initial conditions can be computed by the Load Flow tool or the Machine Initialization tool in the powergui block.

Simulate saturation — Simulate magnetic saturation

off (default) | on

Whether to simulate magnetic saturation of the rotor and stator iron.

Select this check box to provide the matrix of parameters for simulating the saturation.

Clear this check box to not model saturation in your simulation. In this case, the relationship between the stator current and the stator voltage is linear.

[ i(Arms) ; v(VLL rms)] — No-load saturation curve parameters

[14.03593122, 27.81365428, 53.79336849, 72.68890987, 97.98006896, 148.6815601, 215.7428561, 302.9841135, 428.7778367 ; 230, 322, 414, 460, 506, 552, 598, 644, 690] (default) | matrix

No-load saturation curve parameters. The magnetic saturation of the stator and rotor iron (the saturation of the mutual flux) is modeled by a piecewise linear relationship specifying points of the no-load saturation curve. The first row of this matrix contains the values of stator currents. The second row contains values of corresponding terminal voltages (stator voltages). The first point (first column of the matrix) must be different from [0,0]. This point corresponds to the point where the effect of saturation begins.

Click Plot to view the specified no-load saturation curve.

Dependencies

To enable this parameter, select Simulate saturation.

Parameters for Asynchronous Machine pu Units Block

Tip

This tab contains the electrical parameters of the machine. To estimate the electrical parameters of a double-cage asynchronous machine based on standard manufacturer specifications, use the power_AsynchronousMachineParams function.

Nominal power, voltage (line-line), and frequency [ Pn(VA),Vn(Vrms),fn(Hz) ] — Nominal power, voltage, and frequency

[3730 460 60] (default) | three-element vector

Nominal apparent power Pn (VA), RMS line-to-line voltage Vn (V), and frequency fn (Hz).

Vrotor/Vstator voltage ratio — Voltage ratio

1 (default) | positive scalar

Vrotor/Vstator voltage ratio of the wound-rotor asynchronous machine when the rotor is at standstill. Specifying this parameter allows you to get the desired rotor voltage without connecting a transformer at the rotor terminals.

Dependencies

To enable this parameter, in the Configuration tab, set Rotor type to Wound.

Stator resistance and inductance [ Rs,Lls ] (pu) — Stator resistance and leakage inductance

[0.01965 0.0397] (default) | two-element vector

Stator resistance Rs (pu) and leakage inductance Lls (pu).

Rotor resistance and inductance [ Rr',Llr' ] (pu) — Rotor resistance and leakage inductance

[0.01909 0.0397] (default) | two-element vector

Rotor resistance Rr' (pu) and leakage inductance Llr' (pu), both referred to the stator.

Dependencies

To enable this parameter, in the Configuration tab, set Rotor type to Wound or Squirrel-cage.

Cage 1 resistance and inductance [ Rr1',Llr1' ] (pu) — Rotor resistance and leakage inductance

[0.01909 0.0397] (default) | two-element vector

Rotor resistance Rr1' (pu) and leakage inductance Llr1' (pu), both referred to the stator.

Dependencies

To enable this parameter, in the Configuration tab, set Rotor type to Double squirrel-cage.

Cage 2 resistance and inductance [ Rr2',Llr2' ] (pu) — Rotor resistance and leakage inductance

[0.01909 0.0397] (default) | two-element vector

Rotor resistance Rr2' (pu) and leakage inductance Llr2' (pu), both referred to the stator.

Dependencies

To enable this parameter, in the Configuration tab, set Rotor type to Double squirrel-cage.

Mutual inductance Lm (pu) — Magnetizing inductance

1.354 (default) | scalar

Magnetizing inductance Lm (pu).

Inertia constant, friction factor, pole pairs [ H(s) F(pu) p() ] — Inertia constant, friction factor, pole pairs

[0.09526 0.05479 2] (default) | three-element vector

Inertia constant H (s), combined viscous friction coefficient F (pu), and pole pairs p.

Initial conditions — Initial slip s, electrical angle, stator current magnitude, phase angles, rotor current magnitude, and phase angles

[ 1,0 0,0,0 0,0,0 ] (default) | eight-element vector

Initial slip s, electrical angle Θe (degrees), stator current magnitude (pu), and phase angles (degrees):

[slip, th, ias, ibs, ics, phaseas, phasebs, phasecs]

If the Rotor type parameter (in the Configuration tab) is set to Wound, you can also specify optional initial values for the rotor current magnitude (pu), and phase angles (degrees):

[slip, th, ias, ibs, ics, phaseas, phasebs, phasecs, iar, ibr, icr, phasear, phasebr, phasecr]

When the Rotor type parameter (in the Configuration tab) is set to Squirrel-cage, the initial conditions can be computed by the Load Flow tool or the Machine Initialization tool in the powergui block.

Simulate saturation — Simulate magnetic saturation

off (default) | on

Whether to simulate the magnetic saturation of the rotor and stator iron.

Select this check box to provide the matrix of parameters for simulating the saturation.

Clear this check box to not model saturation in your simulation. In this case, the relationship between the stator current and the stator voltage is linear.

[ i; v] (pu) — No-load saturation curve parameters

[0.212,0.4201,0.8125,1.0979,1.4799,2.2457,3.2586,4.5763,6.4763 ; 0.5,0.7,0.9,1,1.1,1.2 ,1.3,1.4,1.5] (default) | matrix

No-load saturation curve parameters. The magnetic saturation of the stator and rotor iron (the saturation of the mutual flux) is modeled by a piecewise linear relationship specifying points of the no-load saturation curve. The first row of this matrix contains the values of stator currents. The second row contains values of corresponding terminal voltages (stator voltages). The first point (first column of the matrix) must be different from [0,0]. This point corresponds to the point where the effect of saturation begins.

Click Plot to view the specified no-load saturation curve.

Dependencies

To enable this parameter, select Simulate saturation.

Advanced

To enable the Advanced tab, in the powergui block, set Simulation type to Discrete and clear Automatically handle Discrete solver and Advanced tab solver settings of blocks.

Sample time (-1 for inherited) — Sample time for block

-1 (default) | scalar

Sample time used by the block. To inherit the sample time specified in the powergui block, set this parameter to –1.

Discrete solver model — Integration method

Trapezoidal non iterative (default) | Trapezoidal iterative (alg. loop) | Trapezoidal robust | Backward Euler robust

Integration method used by the block when the Solver type parameter of the powergui block is set to Discrete.

The Discrete solver model is automatically set to Trapezoidal robust when you select the Automatically handle Discrete solver and Advanced tab solver settings of blocks parameter of the powergui block.

The Trapezoidal non iterative and Trapezoidal iterative (alg. loop) methods are no longer recommended for discretizing the Asynchronous Machine blocks. Trapezoidal non iterative requires you to add a non-negligible shunt load at the machine terminals to guarantee simulation stability, and Trapezoidal iterative (alg. loop) may fail to converge and cause the simulation to stop when the number of machines increases in the model.

The Trapezoidal robust and Backward Euler robust methods allow you to eliminate the need to use parasitic loads and simulate a machine without loads. To eliminate topological errors of machines connected to an inductive circuit (for example, a circuit breaker connected in series with the machine) the machine models a negligible internal load of 0.01% of nominal power.

The Trapezoidal robust method is slightly more accurate than the Backward Euler robust method, especially when the model is simulated at larger sample times. The Trapezoidal robust method may produce slight damped numerical oscillations on machine voltage in no-load conditions, while the Backward Euler robust method prevents oscillations and maintains good accuracy.

For more information on what method you should use in your application, see Simulating Discretized Electrical Systems.

Load Flow

The parameter on this tab is used by the Load Flow tool of the powergui block. These load flow parameter is used for model initialization only. It has no impact on the block model or on the simulation performance.

Mechanical power (W) — Mechanical power applied to machine shaft

scalar

Mechanical power applied to the machine shaft, in watts. When the machine operates in motor mode, specify a positive value. When the machine operates in generator mode, specify a negative value.

For the Asynchronous Machine SI Units block, the default value is 1.492e+006. For the Asynchronous Machine pu Units block, the default value is 0.

Examples

Example 1: Use of the Asynchronous Machine Block in Motor Mode

The power_pwm example uses a Asynchronous Machine block in motor mode. The example consists of an asynchronous machine in an open-loop speed control system.

The machine 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. The base frequency of the sinusoidal reference wave is set at 60 Hz and the triangular carrier wave frequency is set at 1980 Hz. This frequency corresponds to a frequency modulation factor m_f of 33 (60 Hz x 33 = 1980).

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 seconds.

The parameters of the machine are the same as the Asynchronous Machine SI Units block, except for the stator leakage inductance, which is set to twice the normal value 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 example. In the simulation parameters, 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 be seen in the stator and rotor currents.

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 example illustrates the effect of saturation of the Asynchronous Machine block.

Two identical three-phase motors (50 HP, 460 V, and 1800 rpm) are simulated, with and without saturation, to observe the saturation effects on the stator currents. Two different simulations are realized in the example.

The first simulation is the no-load steady-state test. This table 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		Measurements
Vsat (Vrms L-L)	Isat (peak A)	Vrms L-L	Is_A (peak A)
-	-	120	7.322
230	14.04	230	14.03
-	-	250	16.86
-	-	300	24.04
322	27.81	322	28.39
-	-	351	35.22
-	-	382	43.83
414	53.79	414	54.21
-	-	426	58.58
-	-	449	67.94
460	72.69	460	73.01
-	-	472	79.12
-	-	488	88.43
506	97.98	506	100.9
-	-	519	111.6
-	-	535	126.9
-	-	546	139.1
552	148.68	552	146.3
-	-	569	169.1
-	-	581	187.4
598	215.74	598	216.5
-	-	620	259.6
-	-	633	287.8
644	302.98	644	313.2
-	-	659	350
-	-	672	383.7
-	-	681	407.9
690	428.78	690	432.9

The next graph illustrates these results and shows the accuracy of the saturation model. The measured operating points fit well the curve that is plotted from the saturation parameters data.

You can observe the other effects of saturation on the stator currents by running the simulation with a blocked rotor or with many different values of load torque.

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, Section 8.4.1.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced before R2006a