The double phase asynchronous machine is modelled as a Norton equivalent which has a direct interface with the network component. The machine electrical parameters must be specified with real parameters (SI). The control of the machine can only be done externally through the mechanical speed or the mechanical torque.

The double phase asynchronous machine does not participate in the load flow.

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 Tab: 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

Name	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	-
Rqs	Main winding resistance	Ohm
Rds	Auxiliary winding resistance	Ohm
Llqs	Main winding leakage inductance	H
Llds	Auxiliary winding leakage inductance	H
Lmd	d-axis mutual inductance	H
Lmq	q-axis mutual inductance	H
Rqr	Rotor cage resistance, main winding	Ohm
Rdr	Rotor cage resistance, auxiliary winding	Ohm
Llqr	Rotor cage leakage inductance, main winding	H
Lldr	Rotor cage leakage inductance, auxiliary winding	H
Initial slip	Initial slip	-
Nds/Nqs	Turn ratio between auxiliary and main windings	-

Mechanical Data tab

Name	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

Name	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

Name	Description
M+	Stator main winding input connector of the machine. It supports single-phase connection.
M	Stator main winding output connector of the machine. It supports single-phase connection.
A+	Stator auxiliary winding input connector of the machine. It supports single-phase connection.
A	Stator auxiliary winding output connector of the machine. It supports single-phase connection.

Inputs

Name	Description	Unit
	Torque or speed signal if the control is external	Nm or rad/s

Outputs

None

Sensors

Name	Description	Unit
Fluxdr1	d-axis rotor flux, auxiliary winding	V.s
Fluxds	d-axis stator flux, auxiliary winding	V.s
Fluxm	Mutual magnetization flux	V.s
Fluxmd	d-axis mutual magnetization flux, auxiliary winding	V.s
Fluxmq	q-axis mutual magnetization flux, main wnding	V.s
Fluxqr1	q-axis rotor flux, main winding	V.s
Fluxqs	d-axis stator flux, main winding	V.s
Iar1	Phase A rotor current	A
Ibr1	Phase B rotor current	A
Idr1	d-axis rotor current, auxiliary winding	A
Ids	d-axis stator current, auxiliary winding	A
Im	Magnetization current	A
Imd	d-axis magnetization current	A
Imq	q-axis magnetization current	A
Iqr1	q-axis rotor current, main winding	A
Iqs	q-axis stator current, main winding	A
Ps	Active power	W
Slip	slip
ThetaR	Electrical angle of the rotor	rad
Tmec	Mechanical torque	Nm
Tmec_i	Load torque	Nm
Wm	Mechanical speed	rad/s
Wr	Electrical speed	rad/s
Wrpm	Mechanical speed	rpm

Additional Information & Model Equations

The equations below describe the 2-phase single cage asynchronous machine in the dq frame of reference and where all the parameters and variables are reported on the stator side.
The equations of the electrical system are given by:

Where,

The electromagnetic torque and the dynamic equation are described as follows:

Limitations

This model does not account for iron losses.

References

Analysis of Electric Machinery and Drive Systems, 2^nd edition, Paul C. Krause, Oleg Wasynczuk, Scott D. Sudhoff.

HYPERSIM Documentation

Double Phase Asynchronous Machine