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Asynchronous Machine
The asynchronous machine block can be squirrel cage (1-rotor or 2-rotor) or wound rotor machine. The model is a Norton equivalent that interfaces directly with network elements. The model allows to model the following phenomena:
- Independent d and q axes saturation
- The mutual inductance of d and q axes can be unequal
- The stator windings can be configured to be star connected with a common neutral or delta
- The coupling between the cages in the case of the double cage machine
- The transformation ratio between the stator and rotor coils is taken into account
The asynchronous machine participates in the load-flow as a constant positive impedance that is a function of the slip. Therefore, the user must provide the initial slip that corresponds to the steady state of the machine.
Mask and Parameters
The mask of the machine has three tabs:
- Electrical parameters: General parameters of the machine
- Mechanical data: Mechanical parameters of the machine
- Saturation: Parameters of the saturation curve
In the Saturation tab, the user must specify the points of the saturation curve if this is taken into account. In the case of the independent saturation of axes d and q, the two tables represent the positive part of the curve (the negative part is deduced by symmetry) and the number of points of these curves can be different. In the case of total saturation, only the d axis table is used.
Note: The first of each saturation curve must not be zero and corresponds to the linear inductance of the machine in the case of independent saturation.
Electrical Parameters Tab
Variable | Description | Unit | Variable = {Possible Values} |
---|---|---|---|
Base power | Nominal power | kVA | |
Base voltage | Nominal voltage (line to line) | kV | |
Frequency | Nominal frequency | Hz | |
Number of poles | Number of poles | - | |
Rotor type | Wound rotor or cage rotor (single or double) | - | |
DQ speed reference | dq axis reference frame of the machine | - | |
Stator connection | Stator windings connection (wye or delta) | - | |
Rs | Stator resistance | Ohm | |
Lls | Stator leakage inductance | Henry | |
Rr1 | Cage 1 rotor resistance | Ohm | |
Llr1 | Cage 1 leakage inductance | Henry | |
Rr2 | Cage 2 rotor resistance | Ohm | |
Llr2 | Cage 2 leakage inductance | Henry | |
Lmq | q-axis mutual inductance | Henry | |
Lmd | d-axis mutual inductance | Henry | |
Lmr | d and q axes rotor cage mutual inductance | Henry | |
Initial slip | Initial slip | - |
Mechanical Data Tab
Variable | Description | Unit | Variable = {Possible Values} |
---|---|---|---|
Moment of Inertia J | Moment of Inertia | kgm^{2} | |
Friction Kd | Friction coefficient | Nm.s | |
Mechanical torque | User select if the mechanical torque characteristic is internal or external | - | |
Tmec | Torque points of the mechanical torque versus speed | Nm | |
Wmec | Speed points of the mechanical torque versus speed | rad/s |
Saturation Tab
Variable | Description | Unit | Variable = {Possible Values} |
---|---|---|---|
Saturation Enable | User can disable or enable independent or total saturation | - | |
d-axis saturation curve points | Number of d-axis saturation curve points | - | |
Imd | d-axis magnetizing current points of saturation curve. | A | |
Fluxmd | d-axis magnetizing flux points of saturation curve. | Wb | |
q-axis saturation curve points | Number of q-axis saturation curve points | - | |
Imq | q-axis magnetizing current points of saturation curve. | A | |
Fluxmq | q-axis magnetizing flux points of saturation curve. | Wb |
Ports, Inputs, Outputs and Signals Available for Monitoring
Ports
Cage machine
Name | Description |
---|---|
S | AC side stator connector (supports only 3-phase connections) |
N | AC side neutral connector (supports only 1-phase connections) |
Wound rotor machine
Name | Description |
---|---|
S | AC side stator connector (supports only 3-phase connections) |
R | AC side rotor connector (supports only 3-phase connections) |
Ns | AC side network connector (stator neutral). It supports single-phase connection |
Nr | AC side network connector (rotor neutral). It supports single-phase connection |
Inputs
Name | Description | Unit |
---|---|---|
Tmec_i | Load torque signal if load control is external |
Outputs
None
Sensors
Name | Description | Unit |
---|---|---|
Flux0r1 | Zero sequence rotor Flux of cage 1 | V.s |
Flux0s | Zero sequence stator flux | V.s |
Fluxdr1 | d-axis rotor flux of cage 1 | V.s |
Fluxdr2 | d-axis rotor flux of cage 2 | V.s |
Fluxds | d-axis stator flux | V.s |
Fluxm | Mutual magnetization flux | V.s |
Fluxmd | d-axis mutual magnetization flux | V.s |
Fluxmq | q-axis mutual magnetization flux | V.s |
Fluxqr1 | q-axis rotor flux of cage 1 | V.s |
Fluxqr2 | q-axis rotor flux of cage 2 | V.s |
Fluxqs | d-axis stator flux | V.s |
I0r1 | Zero sequence rotor current of cage 1 | A |
I0s | Zero sequence stator current | A |
Iar1 | Phase A rotor current (cage 1) | A |
Iar2 | Phase A rotor current (cage 2) | A |
Ias | Phase A stator current | A |
Ibr1 | Phase B rotor current (cage 1) | A |
Ibr2 | Phase B rotor current (cage 2) | A |
Ibs | Phase B stator current | A |
Icr1 | Phase C rotor current (cage 1) | A |
Icr2 | Phase C rotor current (cage 2) | A |
Ics | Phase C stator current | A |
Idr1 | d-axis rotor current of cage 1 | A |
Idr2 | d-axis rotor current of cage 2 | A |
Ids | d-axis stator current | A |
Im | Magnetization current | A |
Imd | d-axis magnetization current | A |
Imq | q-axis magnetization current | A |
Iqr1 | q-axis rotor current of cage 1 | A |
Iqr2 | q-axis rotor current of cage 2 | A |
Iqs | q-axis stator current | A |
Ps | Active power | W |
Qs | Reactive power | VAr |
Slip | slip | |
Tmec | Mechanical torque | Nm |
Tmec_i | Load torque | Nm |
V0r1 | Zero sequence rotor voltage of cage 1 | V |
V0s | Zero sequence stator voltage | V |
Vdr1 | d-axis rotor voltage of cage 1 (Not used for squirrel cage machine but useful for future wound rotor machine) | V |
Vds | d-axis stator voltage | V |
Vqr1 | q-axis rotor voltage of cage 1 (Not used for squirrel cage machine but useful for future wound rotor machine) | V |
Vqs | q-axis stator voltage | V |
Wm | Mechanical speed | rad/s |
Wr | Electrical speed | rad/s |
Wrpm | Mechanical speed | rpm |
Additional Information & Model Equations
Model Equations
The equations below describe the double cage machine with mutual coupling between the two cages (due to leakage flux), in the arbitrary reference frame dq0 and where all parameters and variables are referred on the stator side.
The equations of the electrical system are given by:
Electrical Equations
Electrical Equations of the Rotor Cage
Stator flux equations
Rotor flux equations
where
The electromagnetic torque and the mechanical equation are described as follows:
Note: In the case of a one-cage or wound rotor machine the equations for the second cage are not used and the mutual induction between cages is zero. The d and q axis rotor voltages 1 are zero and not zero respectively for the one-cage and wound rotor machine.
Limitations
This model does not account for iron losses.
References
Analysis of Electric Machinery and Drive Systems, 2nd edition, Paul C. Krause, Oleg Wasynczuk, Scott D. Sudhoff
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