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
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
Moment of Inertia J	Moment of Inertia	kgm²
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
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

HYPERSIM Documentation

Asynchronous Machine