Wound Field Synchronous Machine (WFSM)

Symbol

Description

Wound Field Synchronous Machine (WFSM)

Model of a three-phase Wound Field Synchronous Machine (WFSM). In motor operation torque and speed have the same sign. Rotor Angle is defined as the angle between the a-phase and the d-axis. Stator winding is star connected in this model. To access the neutral point pin, check the "Neutral Point" checkbox in the properties menu.

Electrical model and equations

$v_a = R_s i_a + \frac{d}{dt} (L_{aa} i_a + L_{ab} i_b + L_{ac} i_c + L_{amf} i_f )$

$v_b = R_s i_b + \frac{d}{dt} (L_{ba} i_a + L_{bb} i_b + L_{bc} i_c + L_{bmf} i_f )$

$v_c = R_s i_c + \frac{d}{dt} (L_{ca} i_a + L_{cb} i_b + L_{cc} i_c + L_{cmf} i_f )$

$v_f = R_f i_f + \frac{d}{dt} (L_{amf} i_a + L_{bmf} i_b + L_{cmf} i_c + L_{f} i_f )$

Phase inductances ( $L_{aa}$ , $L_{ab}$ , $L_{ac}$ ,..., $L_{cc}$ ) are calculated from the stator inductance in the synchronous reference frame ( $L_{d}$ , $L_{q}$ ) defined in the property panel as the incremental inductance.
Field inductances ( $L_{amf}$ , $L_{bmf}$ , $L_{cmf}$ and $L_{f}$ ) are calculated from the field circuit self- and mututal- inductance ( $L_{f}$ , $M_{fd}$ ).

Electromechanical equations

Electro-magnetic torque:

$T_e = 1.5 * N_{ pp}*(i_q * \phi_d - i_d * \phi_q)$

where $\phi_d = L_d i_d + 2/3 * M_{fd} * i_f$ and $\phi_q = L_q i_q$

Mechanical rotational speed $\Omega$ :

$J \frac{d\Omega}{ dt} = T_e - B \Omega$

Library

Electrical > Motors

Parameters

Property	Display Name	Parameter Type	Description
Rs	Rs - Stator Resistance [Ohm]	DoubleParameter	Stator Winding Resistance [Ohm]
Rf	Rf - Rotor Resistance [Ohm]	DoubleParameter	Stator Winding Resistance [Ohm]
Ld	Ld - Direct Axis Inductance [H]	DoubleMatrixParameter	Direct Axis Inductance [H]
Lq	Lq - Quadratic Axis Inductance [H]	DoubleMatrixParameter	Quadratic Axis Inductance [H]
J	J - Rotor Inertia [kg.m²]	DoubleParameter	Rotor Inertia [kg.m²]
B	B - Rotor Friction Coefficient [N.m/(rad/s)]	DoubleParameter	Rotor Friction Coefficient [N.m/(rad/s)]
InitialSpeed	Rotor Initial Speed [rad/s]	DoubleParameter	Rotor initial speed [ rad/s]
InitialCurrent	Initial Current [A]	DoubleArrayParameter	Initial Current Vector [IA IB IC]
NPP	NPP - Poles pairs	IntParameter	Number of pole pairs
ExposeNeutralPoint	Neutral Point	BoolParameter	Expose Neutral Point (Boolean)
Use2DTable	use 2D inductance table	BoolParameter	Use 2D inductance table (Boolean)
Lf	Lf - Field Circuit Self-Inductance [H]	DoubleMatrixParameter	Field Circuit Inductance [H]
Mfd	Mfd - Field Circuit Mutual-Inductance [H]	DoubleMatrixParameter	Field Circuit Inductance [H]

Pins

Property	Pin Name	Type	Description
Pin_A	A	Electrical	Phase A (Electrical)
Pin_B	B	Electrical	Phase B (Electrical)
Pin_C	C	Electrical	Phase C (Electrical)
Pin_F	F	Electrical	Field (Electrical)
Pin_R	R	RotationalMechanical	Rotor (Rotational Mechanical)
Pin_Angle	Angle	ControlOut	Rotor Angle in radians, electrical angle (Control)

Default Size

Width	Height
8	8