# Asynchronous Machine

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

• Library:
• 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

Vqs = Rsiqs + dφqs/dt + ωφds

Vds = Rsids + dφds/dtωφqs

V'qr = R'ri'qr + dφ'qr/dt + (ωωr)φ'dr

V'dr = R'ri'dr + dφ'dr/dt – (ωωr)φ'qr

Te = 1.5p(φdsiqsφqsids)

ω — Reference frame angular velocity

ωr — Electrical angular velocity

φqs = Lsiqs + Lmi'qr

φds = Lsids + Lmi'dr

φ'qr = L'ri'qr + Lmiqs

φ'dr = L'ri'dr + Lmids

Ls = Lls + Lm

L'r = L'lr + Lm

### Electrical System of the Double Squirrel-Cage Machine

Vqs = Rsiqs + dφqs/dt + ωφds

Vds = Rsids + dφds/dtωφqs

0 = R'r1i'qr1 + dφ'qr1/dt + (ωωr)φ'dr1

0 = R'r1i'dr1 + dφ'dr1/dt – (ωωr)φ'qr1

0 = R'r2i'qr2 + dφ'qr2/dt + (ωωr)φ'dr2

0 = R'r2i'dr2 + dφ'dr2/dt – (ωωr)φ'qr2

Te = 1.5p(φdsiqsφqsids)

φqs = Lsiqs + Lm(i'qr1 + i'qr2)

φds = Lsids + Lm(i'dr1 + i'dr2)

φ'qr1 = L'r1i'qr1 + Lmiqs

φ'dr1 = L'r1i'dr1 + Lmids

φ'qr2 = L'r2i'qr2 + Lmiqs

φ'dr2 = L'r2i'dr2 + Lmids

Ls = Lls + Lm

L'r1 = L'lr1 + Lm

L'r2 = L'lr2 + Lm

### 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

expand all

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.

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

expand all

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

Te

Electromagnetic torque Te

N.m or pu

theta

Rotor angle thetam

### Conserving

expand all

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

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

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

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

#### Dependencies

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

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

#### Dependencies

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

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

#### Dependencies

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

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

expand all

### Configuration

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.

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.

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.

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 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.

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

In the preceding equations, Θ is the angular position of the reference frame, while β = θ – θr 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.

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

The table shows the values taken by Θ and β in each reference frame (Θe 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 SettingAsynchronous Machine Block SettingReference frame Parameter
Simulation type is set to Phasor or Discrete PhasorSynchronous
Simulation type is set to Discrete and the Automatically handle Discrete solver and Advanced tab solver settings of blocks parameter is selectedRotor
Simulation type is set to Discrete Discrete solver model is set to Trapezoidal robust or Backward Euler robustRotor

#### 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).

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

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

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.

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.

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.

Magnetizing inductance Lm (H).

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 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.

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.

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

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

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.

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.

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.

Magnetizing inductance Lm (pu).

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

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.

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.

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.

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

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.

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 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 mf 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.